diff --git a/src/03_basic_sets/module.jl b/src/03_basic_sets/module.jl
deleted file mode 100644
index e7a9c321c..000000000
--- a/src/03_basic_sets/module.jl
+++ /dev/null
@@ -1,15 +0,0 @@
-module BasicSets 
-
-using Reexport
-
-include("01_sets/module.jl") # Categories
-include("02_finsets/module.jl") # 1
-include("03_setfunctions/module.jl") # 2
-include("04_finfunctions/module.jl") # 3
-
-@reexport using .Sets
-@reexport using .FinSets
-@reexport using .SetFunctions
-@reexport using .FinFunctions
-
-end # module
diff --git a/src/04_categorical_algebra/01_cats/module.jl b/src/04_categorical_algebra/01_cats/module.jl
deleted file mode 100644
index 006a7de2f..000000000
--- a/src/04_categorical_algebra/01_cats/module.jl
+++ /dev/null
@@ -1,44 +0,0 @@
-module Cats 
-
-using Reexport
-
-include("01_paths/Paths.jl") # [DEPS]
-@reexport using .Paths
-
-include("02_categories/module.jl") #
-@reexport using .Categories
-
-include("03_fincats/module.jl") # 2
-@reexport using .FinCats
-
-include("04_functors/module.jl") # 2
-@reexport using .Functors
-
-include("05_freediagrams/module.jl") # 3
-@reexport using .FreeDiagrams
-
-include("06_finfunctors/module.jl") # 2, 5
-@reexport using .FinFunctors
-
-include("07_cat_of_cat/CatOfCat.jl") # 2
-@reexport using .CatOfCat
-
-include("08_natural_transformations/module.jl")
-@reexport using .Transformations
-
-include("09_limits_colimits/module.jl") # 4,5
-@reexport using .LimitsColimits
-
-include("10_commutative_diagrams/CommutativeDiagrams.jl")
-@reexport using .CommutativeDiagrams
-
-include("11_diagrams/module.jl") # 5
-@reexport using .Diagrams
-
-include("12_slice/module.jl")
-@reexport using .SliceCategories
-
-include("13_subobjects/Subobjects.jl") # Limits
-@reexport using .Subobjects
-
-end # module
diff --git a/src/04_categorical_algebra/03_pointwise/module.jl b/src/04_categorical_algebra/03_pointwise/module.jl
deleted file mode 100644
index 09fe7ec08..000000000
--- a/src/04_categorical_algebra/03_pointwise/module.jl
+++ /dev/null
@@ -1,36 +0,0 @@
-module Pointwise 
-using Reexport
-
-include("01_acsettransformations/ACSetTransformations.jl")
-@reexport using .ACSetTransformations
-
-include("02_csets/module.jl")
-@reexport using .CSets
-
-include("03_pointwisecats/module.jl")
-@reexport using .PointwiseCats
-
-include("04_limits_colimits/module.jl")
-@reexport using .LimitsColimits
-
-include("05_homsearch/module.jl")
-@reexport using .HomSearch
-
-include("06_catelements/CatElements.jl")
-@reexport using .CatElements
-
-include("07_subcsets/SubCSets.jl")
-@reexport using .SubCSets
-
-
-include("08_chase/Chase.jl")
-@reexport using .Chase
-
-include("09_datamigrations/module.jl")
-@reexport using .FunctorialDataMigrations
-
-
-include("10_structured_cospans/StructuredCospans.jl")
-@reexport using .StructuredCospans
-
-end # module
diff --git a/src/04_categorical_algebra/module.jl b/src/04_categorical_algebra/module.jl
deleted file mode 100644
index 9f86fe8cb..000000000
--- a/src/04_categorical_algebra/module.jl
+++ /dev/null
@@ -1,18 +0,0 @@
-module CategoricalAlgebra
-
-using Reexport
-
-include("01_cats/module.jl") 
-@reexport using .Cats
-
-include("02_setcats/module.jl") # depends on Cats
-@reexport using .SetCats
-
-include("03_pointwise/module.jl") # depends on Cats, SetCats
-@reexport using .Pointwise
-
-include("04_misc/module.jl") # doesn't depend on the other three
-
-@reexport using .Misc
-
-end # module
diff --git a/src/Catlab.jl b/src/Catlab.jl
index 0e8567bd2..3db16ae3d 100644
--- a/src/Catlab.jl
+++ b/src/Catlab.jl
@@ -2,11 +2,11 @@ module Catlab
 
 using Reexport
 
-include("01_theories/module.jl")
+include("theories/module.jl")
 include("ACSetsGATsInterop.jl") # depends on Theories but is not a theory
-include("02_graphs/Graphs.jl")
-include("03_basic_sets/module.jl")
-include("04_categorical_algebra/module.jl")
+include("graphs/Graphs.jl")
+include("basic_sets/module.jl")
+include("categorical_algebra/module.jl")
 include("wiring_diagrams/WiringDiagrams.jl")
 include("graphics/Graphics.jl")
 include("programs/Programs.jl")
diff --git a/src/03_basic_sets/04_finfunctions/FinFnDict.jl b/src/basic_sets/finfunctions/FinFnDict.jl
similarity index 100%
rename from src/03_basic_sets/04_finfunctions/FinFnDict.jl
rename to src/basic_sets/finfunctions/FinFnDict.jl
diff --git a/src/03_basic_sets/04_finfunctions/FinFnVector.jl b/src/basic_sets/finfunctions/FinFnVector.jl
similarity index 100%
rename from src/03_basic_sets/04_finfunctions/FinFnVector.jl
rename to src/basic_sets/finfunctions/FinFnVector.jl
diff --git a/src/03_basic_sets/04_finfunctions/FinForce.jl b/src/basic_sets/finfunctions/FinForce.jl
similarity index 100%
rename from src/03_basic_sets/04_finfunctions/FinForce.jl
rename to src/basic_sets/finfunctions/FinForce.jl
diff --git a/src/03_basic_sets/04_finfunctions/FinFunctions.jl b/src/basic_sets/finfunctions/FinFunctions.jl
similarity index 100%
rename from src/03_basic_sets/04_finfunctions/FinFunctions.jl
rename to src/basic_sets/finfunctions/FinFunctions.jl
diff --git a/src/03_basic_sets/04_finfunctions/module.jl b/src/basic_sets/finfunctions/module.jl
similarity index 100%
rename from src/03_basic_sets/04_finfunctions/module.jl
rename to src/basic_sets/finfunctions/module.jl
diff --git a/src/03_basic_sets/02_finsets/EitherFinSet.jl b/src/basic_sets/finsets/EitherFinSet.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/EitherFinSet.jl
rename to src/basic_sets/finsets/EitherFinSet.jl
diff --git a/src/03_basic_sets/02_finsets/EmptySets.jl b/src/basic_sets/finsets/EmptySets.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/EmptySets.jl
rename to src/basic_sets/finsets/EmptySets.jl
diff --git a/src/03_basic_sets/02_finsets/FinSetHash.jl b/src/basic_sets/finsets/FinSetHash.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/FinSetHash.jl
rename to src/basic_sets/finsets/FinSetHash.jl
diff --git a/src/03_basic_sets/02_finsets/FinSetInts.jl b/src/basic_sets/finsets/FinSetInts.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/FinSetInts.jl
rename to src/basic_sets/finsets/FinSetInts.jl
diff --git a/src/03_basic_sets/02_finsets/FinSetVect.jl b/src/basic_sets/finsets/FinSetVect.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/FinSetVect.jl
rename to src/basic_sets/finsets/FinSetVect.jl
diff --git a/src/03_basic_sets/02_finsets/FinSets.jl b/src/basic_sets/finsets/FinSets.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/FinSets.jl
rename to src/basic_sets/finsets/FinSets.jl
diff --git a/src/03_basic_sets/02_finsets/ProdFinSets.jl b/src/basic_sets/finsets/ProdFinSets.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/ProdFinSets.jl
rename to src/basic_sets/finsets/ProdFinSets.jl
diff --git a/src/03_basic_sets/02_finsets/SIngletonSets.jl b/src/basic_sets/finsets/SingletonSets.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/SIngletonSets.jl
rename to src/basic_sets/finsets/SingletonSets.jl
diff --git a/src/03_basic_sets/02_finsets/SumFinSets.jl b/src/basic_sets/finsets/SumFinSets.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/SumFinSets.jl
rename to src/basic_sets/finsets/SumFinSets.jl
diff --git a/src/03_basic_sets/02_finsets/TabularSet.jl b/src/basic_sets/finsets/TabularSet.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/TabularSet.jl
rename to src/basic_sets/finsets/TabularSet.jl
diff --git a/src/03_basic_sets/02_finsets/module.jl b/src/basic_sets/finsets/module.jl
similarity index 100%
rename from src/03_basic_sets/02_finsets/module.jl
rename to src/basic_sets/finsets/module.jl
diff --git a/src/basic_sets/module.jl b/src/basic_sets/module.jl
new file mode 100644
index 000000000..c1ca2b54d
--- /dev/null
+++ b/src/basic_sets/module.jl
@@ -0,0 +1,17 @@
+module BasicSets 
+
+using Reexport
+
+include("sets/module.jl")
+@reexport using .Sets
+
+include("finsets/module.jl")
+@reexport using .FinSets
+
+include("setfunctions/module.jl")
+@reexport using .SetFunctions
+
+include("finfunctions/module.jl")
+@reexport using .FinFunctions
+
+end # module
diff --git a/src/03_basic_sets/03_setfunctions/Callable.jl b/src/basic_sets/setfunctions/Callable.jl
similarity index 100%
rename from src/03_basic_sets/03_setfunctions/Callable.jl
rename to src/basic_sets/setfunctions/Callable.jl
diff --git a/src/03_basic_sets/03_setfunctions/CompFunction.jl b/src/basic_sets/setfunctions/CompFunction.jl
similarity index 100%
rename from src/03_basic_sets/03_setfunctions/CompFunction.jl
rename to src/basic_sets/setfunctions/CompFunction.jl
diff --git a/src/03_basic_sets/03_setfunctions/ConstEither.jl b/src/basic_sets/setfunctions/ConstEither.jl
similarity index 100%
rename from src/03_basic_sets/03_setfunctions/ConstEither.jl
rename to src/basic_sets/setfunctions/ConstEither.jl
diff --git a/src/03_basic_sets/03_setfunctions/ConstFn.jl b/src/basic_sets/setfunctions/ConstFn.jl
similarity index 100%
rename from src/03_basic_sets/03_setfunctions/ConstFn.jl
rename to src/basic_sets/setfunctions/ConstFn.jl
diff --git a/src/03_basic_sets/03_setfunctions/Force.jl b/src/basic_sets/setfunctions/Force.jl
similarity index 100%
rename from src/03_basic_sets/03_setfunctions/Force.jl
rename to src/basic_sets/setfunctions/Force.jl
diff --git a/src/03_basic_sets/03_setfunctions/IdFunction.jl b/src/basic_sets/setfunctions/IdFunction.jl
similarity index 100%
rename from src/03_basic_sets/03_setfunctions/IdFunction.jl
rename to src/basic_sets/setfunctions/IdFunction.jl
diff --git a/src/03_basic_sets/03_setfunctions/PredFn.jl b/src/basic_sets/setfunctions/PredFn.jl
similarity index 100%
rename from src/03_basic_sets/03_setfunctions/PredFn.jl
rename to src/basic_sets/setfunctions/PredFn.jl
diff --git a/src/03_basic_sets/03_setfunctions/SetFunctions.jl b/src/basic_sets/setfunctions/SetFunctions.jl
similarity index 100%
rename from src/03_basic_sets/03_setfunctions/SetFunctions.jl
rename to src/basic_sets/setfunctions/SetFunctions.jl
diff --git a/src/03_basic_sets/03_setfunctions/module.jl b/src/basic_sets/setfunctions/module.jl
similarity index 100%
rename from src/03_basic_sets/03_setfunctions/module.jl
rename to src/basic_sets/setfunctions/module.jl
diff --git a/src/03_basic_sets/01_sets/EitherSets.jl b/src/basic_sets/sets/EitherSets.jl
similarity index 100%
rename from src/03_basic_sets/01_sets/EitherSets.jl
rename to src/basic_sets/sets/EitherSets.jl
diff --git a/src/03_basic_sets/01_sets/PredSet.jl b/src/basic_sets/sets/PredSet.jl
similarity index 100%
rename from src/03_basic_sets/01_sets/PredSet.jl
rename to src/basic_sets/sets/PredSet.jl
diff --git a/src/03_basic_sets/01_sets/ProdSets.jl b/src/basic_sets/sets/ProdSets.jl
similarity index 100%
rename from src/03_basic_sets/01_sets/ProdSets.jl
rename to src/basic_sets/sets/ProdSets.jl
diff --git a/src/03_basic_sets/01_sets/Sets.jl b/src/basic_sets/sets/Sets.jl
similarity index 100%
rename from src/03_basic_sets/01_sets/Sets.jl
rename to src/basic_sets/sets/Sets.jl
diff --git a/src/03_basic_sets/01_sets/SumSets.jl b/src/basic_sets/sets/SumSets.jl
similarity index 100%
rename from src/03_basic_sets/01_sets/SumSets.jl
rename to src/basic_sets/sets/SumSets.jl
diff --git a/src/03_basic_sets/01_sets/TypeSet.jl b/src/basic_sets/sets/TypeSet.jl
similarity index 100%
rename from src/03_basic_sets/01_sets/TypeSet.jl
rename to src/basic_sets/sets/TypeSet.jl
diff --git a/src/03_basic_sets/01_sets/UnionSet.jl b/src/basic_sets/sets/UnionSet.jl
similarity index 100%
rename from src/03_basic_sets/01_sets/UnionSet.jl
rename to src/basic_sets/sets/UnionSet.jl
diff --git a/src/03_basic_sets/01_sets/module.jl b/src/basic_sets/sets/module.jl
similarity index 100%
rename from src/03_basic_sets/01_sets/module.jl
rename to src/basic_sets/sets/module.jl
diff --git a/src/04_categorical_algebra/01_cats/07_cat_of_cat/CatOfCat.jl b/src/categorical_algebra/cats/cat_of_cat/CatOfCat.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/07_cat_of_cat/CatOfCat.jl
rename to src/categorical_algebra/cats/cat_of_cat/CatOfCat.jl
diff --git a/src/04_categorical_algebra/01_cats/02_categories/Categories.jl b/src/categorical_algebra/cats/categories/Categories.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/02_categories/Categories.jl
rename to src/categorical_algebra/cats/categories/Categories.jl
diff --git a/src/04_categorical_algebra/01_cats/02_categories/CoproductCats.jl b/src/categorical_algebra/cats/categories/CoproductCats.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/02_categories/CoproductCats.jl
rename to src/categorical_algebra/cats/categories/CoproductCats.jl
diff --git a/src/04_categorical_algebra/01_cats/02_categories/DiscreteCats.jl b/src/categorical_algebra/cats/categories/DiscreteCats.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/02_categories/DiscreteCats.jl
rename to src/categorical_algebra/cats/categories/DiscreteCats.jl
diff --git a/src/04_categorical_algebra/01_cats/02_categories/OpCats.jl b/src/categorical_algebra/cats/categories/OpCats.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/02_categories/OpCats.jl
rename to src/categorical_algebra/cats/categories/OpCats.jl
diff --git a/src/04_categorical_algebra/01_cats/02_categories/TrivialCats.jl b/src/categorical_algebra/cats/categories/TrivialCats.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/02_categories/TrivialCats.jl
rename to src/categorical_algebra/cats/categories/TrivialCats.jl
diff --git a/src/04_categorical_algebra/01_cats/02_categories/TypeCats.jl b/src/categorical_algebra/cats/categories/TypeCats.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/02_categories/TypeCats.jl
rename to src/categorical_algebra/cats/categories/TypeCats.jl
diff --git a/src/04_categorical_algebra/01_cats/02_categories/module.jl b/src/categorical_algebra/cats/categories/module.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/02_categories/module.jl
rename to src/categorical_algebra/cats/categories/module.jl
diff --git a/src/04_categorical_algebra/01_cats/10_commutative_diagrams/CommutativeDiagrams.jl b/src/categorical_algebra/cats/commutative_diagrams/CommutativeDiagrams.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/10_commutative_diagrams/CommutativeDiagrams.jl
rename to src/categorical_algebra/cats/commutative_diagrams/CommutativeDiagrams.jl
diff --git a/src/04_categorical_algebra/01_cats/11_diagrams/Diagrams.jl b/src/categorical_algebra/cats/diagrams/Diagrams.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/11_diagrams/Diagrams.jl
rename to src/categorical_algebra/cats/diagrams/Diagrams.jl
diff --git a/src/04_categorical_algebra/01_cats/11_diagrams/Limits.jl b/src/categorical_algebra/cats/diagrams/Limits.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/11_diagrams/Limits.jl
rename to src/categorical_algebra/cats/diagrams/Limits.jl
diff --git a/src/04_categorical_algebra/01_cats/11_diagrams/Monads.jl b/src/categorical_algebra/cats/diagrams/Monads.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/11_diagrams/Monads.jl
rename to src/categorical_algebra/cats/diagrams/Monads.jl
diff --git a/src/04_categorical_algebra/01_cats/11_diagrams/module.jl b/src/categorical_algebra/cats/diagrams/module.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/11_diagrams/module.jl
rename to src/categorical_algebra/cats/diagrams/module.jl
diff --git a/src/04_categorical_algebra/01_cats/03_fincats/DiscreteFinCats.jl b/src/categorical_algebra/cats/fincats/DiscreteFinCats.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/03_fincats/DiscreteFinCats.jl
rename to src/categorical_algebra/cats/fincats/DiscreteFinCats.jl
diff --git a/src/04_categorical_algebra/01_cats/03_fincats/FinCatCat.jl b/src/categorical_algebra/cats/fincats/FinCatCat.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/03_fincats/FinCatCat.jl
rename to src/categorical_algebra/cats/fincats/FinCatCat.jl
diff --git a/src/04_categorical_algebra/01_cats/03_fincats/FinCatGraphs.jl b/src/categorical_algebra/cats/fincats/FinCatGraphs.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/03_fincats/FinCatGraphs.jl
rename to src/categorical_algebra/cats/fincats/FinCatGraphs.jl
diff --git a/src/04_categorical_algebra/01_cats/03_fincats/FinCatPres.jl b/src/categorical_algebra/cats/fincats/FinCatPres.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/03_fincats/FinCatPres.jl
rename to src/categorical_algebra/cats/fincats/FinCatPres.jl
diff --git a/src/04_categorical_algebra/01_cats/03_fincats/FinCats.jl b/src/categorical_algebra/cats/fincats/FinCats.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/03_fincats/FinCats.jl
rename to src/categorical_algebra/cats/fincats/FinCats.jl
diff --git a/src/04_categorical_algebra/01_cats/03_fincats/FinCatsAsCats.jl b/src/categorical_algebra/cats/fincats/FinCatsAsCats.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/03_fincats/FinCatsAsCats.jl
rename to src/categorical_algebra/cats/fincats/FinCatsAsCats.jl
diff --git a/src/04_categorical_algebra/01_cats/03_fincats/OpFinCat.jl b/src/categorical_algebra/cats/fincats/OpFinCat.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/03_fincats/OpFinCat.jl
rename to src/categorical_algebra/cats/fincats/OpFinCat.jl
diff --git a/src/04_categorical_algebra/01_cats/03_fincats/PathCats.jl b/src/categorical_algebra/cats/fincats/PathCats.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/03_fincats/PathCats.jl
rename to src/categorical_algebra/cats/fincats/PathCats.jl
diff --git a/src/04_categorical_algebra/01_cats/03_fincats/PreorderCats.jl b/src/categorical_algebra/cats/fincats/PreorderCats.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/03_fincats/PreorderCats.jl
rename to src/categorical_algebra/cats/fincats/PreorderCats.jl
diff --git a/src/04_categorical_algebra/01_cats/03_fincats/module.jl b/src/categorical_algebra/cats/fincats/module.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/03_fincats/module.jl
rename to src/categorical_algebra/cats/fincats/module.jl
diff --git a/src/04_categorical_algebra/01_cats/06_finfunctors/CompFinFunctor.jl b/src/categorical_algebra/cats/finfunctors/CompFinFunctor.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/06_finfunctors/CompFinFunctor.jl
rename to src/categorical_algebra/cats/finfunctors/CompFinFunctor.jl
diff --git a/src/04_categorical_algebra/01_cats/06_finfunctors/FinDomMap.jl b/src/categorical_algebra/cats/finfunctors/FinDomMap.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/06_finfunctors/FinDomMap.jl
rename to src/categorical_algebra/cats/finfunctors/FinDomMap.jl
diff --git a/src/04_categorical_algebra/01_cats/06_finfunctors/FinFunctors.jl b/src/categorical_algebra/cats/finfunctors/FinFunctors.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/06_finfunctors/FinFunctors.jl
rename to src/categorical_algebra/cats/finfunctors/FinFunctors.jl
diff --git a/src/04_categorical_algebra/01_cats/06_finfunctors/IdFinFunctor.jl b/src/categorical_algebra/cats/finfunctors/IdFinFunctor.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/06_finfunctors/IdFinFunctor.jl
rename to src/categorical_algebra/cats/finfunctors/IdFinFunctor.jl
diff --git a/src/04_categorical_algebra/01_cats/06_finfunctors/OpFinFunctor.jl b/src/categorical_algebra/cats/finfunctors/OpFinFunctor.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/06_finfunctors/OpFinFunctor.jl
rename to src/categorical_algebra/cats/finfunctors/OpFinFunctor.jl
diff --git a/src/04_categorical_algebra/01_cats/06_finfunctors/module.jl b/src/categorical_algebra/cats/finfunctors/module.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/06_finfunctors/module.jl
rename to src/categorical_algebra/cats/finfunctors/module.jl
diff --git a/src/04_categorical_algebra/01_cats/05_freediagrams/Bipartite.jl b/src/categorical_algebra/cats/freediagrams/Bipartite.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/05_freediagrams/Bipartite.jl
rename to src/categorical_algebra/cats/freediagrams/Bipartite.jl
diff --git a/src/04_categorical_algebra/01_cats/05_freediagrams/ComposableHoms.jl b/src/categorical_algebra/cats/freediagrams/ComposableHoms.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/05_freediagrams/ComposableHoms.jl
rename to src/categorical_algebra/cats/freediagrams/ComposableHoms.jl
diff --git a/src/04_categorical_algebra/01_cats/05_freediagrams/Discrete.jl b/src/categorical_algebra/cats/freediagrams/Discrete.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/05_freediagrams/Discrete.jl
rename to src/categorical_algebra/cats/freediagrams/Discrete.jl
diff --git a/src/04_categorical_algebra/01_cats/05_freediagrams/FreeDiagrams.jl b/src/categorical_algebra/cats/freediagrams/FreeDiagrams.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/05_freediagrams/FreeDiagrams.jl
rename to src/categorical_algebra/cats/freediagrams/FreeDiagrams.jl
diff --git a/src/04_categorical_algebra/01_cats/05_freediagrams/FreeGraphs.jl b/src/categorical_algebra/cats/freediagrams/FreeGraphs.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/05_freediagrams/FreeGraphs.jl
rename to src/categorical_algebra/cats/freediagrams/FreeGraphs.jl
diff --git a/src/04_categorical_algebra/01_cats/05_freediagrams/Multispans.jl b/src/categorical_algebra/cats/freediagrams/Multispans.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/05_freediagrams/Multispans.jl
rename to src/categorical_algebra/cats/freediagrams/Multispans.jl
diff --git a/src/04_categorical_algebra/01_cats/05_freediagrams/ParallelHoms.jl b/src/categorical_algebra/cats/freediagrams/ParallelHoms.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/05_freediagrams/ParallelHoms.jl
rename to src/categorical_algebra/cats/freediagrams/ParallelHoms.jl
diff --git a/src/04_categorical_algebra/01_cats/05_freediagrams/Specialize.jl b/src/categorical_algebra/cats/freediagrams/Specialize.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/05_freediagrams/Specialize.jl
rename to src/categorical_algebra/cats/freediagrams/Specialize.jl
diff --git a/src/04_categorical_algebra/01_cats/05_freediagrams/module.jl b/src/categorical_algebra/cats/freediagrams/module.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/05_freediagrams/module.jl
rename to src/categorical_algebra/cats/freediagrams/module.jl
diff --git a/src/04_categorical_algebra/01_cats/04_functors/CallFunctor.jl b/src/categorical_algebra/cats/functors/CallFunctor.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/04_functors/CallFunctor.jl
rename to src/categorical_algebra/cats/functors/CallFunctor.jl
diff --git a/src/04_categorical_algebra/01_cats/04_functors/CompFunctor.jl b/src/categorical_algebra/cats/functors/CompFunctor.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/04_functors/CompFunctor.jl
rename to src/categorical_algebra/cats/functors/CompFunctor.jl
diff --git a/src/04_categorical_algebra/01_cats/04_functors/Functors.jl b/src/categorical_algebra/cats/functors/Functors.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/04_functors/Functors.jl
rename to src/categorical_algebra/cats/functors/Functors.jl
diff --git a/src/04_categorical_algebra/01_cats/04_functors/IdFunctor.jl b/src/categorical_algebra/cats/functors/IdFunctor.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/04_functors/IdFunctor.jl
rename to src/categorical_algebra/cats/functors/IdFunctor.jl
diff --git a/src/04_categorical_algebra/01_cats/04_functors/OpFunctor.jl b/src/categorical_algebra/cats/functors/OpFunctor.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/04_functors/OpFunctor.jl
rename to src/categorical_algebra/cats/functors/OpFunctor.jl
diff --git a/src/04_categorical_algebra/01_cats/04_functors/module.jl b/src/categorical_algebra/cats/functors/module.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/04_functors/module.jl
rename to src/categorical_algebra/cats/functors/module.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Coequalizers.jl b/src/categorical_algebra/cats/limits_colimits/Coequalizers.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Coequalizers.jl
rename to src/categorical_algebra/cats/limits_colimits/Coequalizers.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Colimits.jl b/src/categorical_algebra/cats/limits_colimits/Colimits.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Colimits.jl
rename to src/categorical_algebra/cats/limits_colimits/Colimits.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Coproducts.jl b/src/categorical_algebra/cats/limits_colimits/Coproducts.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Coproducts.jl
rename to src/categorical_algebra/cats/limits_colimits/Coproducts.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/EpiMono.jl b/src/categorical_algebra/cats/limits_colimits/EpiMono.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/EpiMono.jl
rename to src/categorical_algebra/cats/limits_colimits/EpiMono.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Equalizers.jl b/src/categorical_algebra/cats/limits_colimits/Equalizers.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Equalizers.jl
rename to src/categorical_algebra/cats/limits_colimits/Equalizers.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/FreeGraphs.jl b/src/categorical_algebra/cats/limits_colimits/FreeGraphs.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/FreeGraphs.jl
rename to src/categorical_algebra/cats/limits_colimits/FreeGraphs.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Initials.jl b/src/categorical_algebra/cats/limits_colimits/Initials.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Initials.jl
rename to src/categorical_algebra/cats/limits_colimits/Initials.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Limits.jl b/src/categorical_algebra/cats/limits_colimits/Limits.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Limits.jl
rename to src/categorical_algebra/cats/limits_colimits/Limits.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/LimitsColimits.jl b/src/categorical_algebra/cats/limits_colimits/LimitsColimits.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/LimitsColimits.jl
rename to src/categorical_algebra/cats/limits_colimits/LimitsColimits.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/MonoidalColimits.jl b/src/categorical_algebra/cats/limits_colimits/MonoidalColimits.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/MonoidalColimits.jl
rename to src/categorical_algebra/cats/limits_colimits/MonoidalColimits.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/MonoidalLimits.jl b/src/categorical_algebra/cats/limits_colimits/MonoidalLimits.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/MonoidalLimits.jl
rename to src/categorical_algebra/cats/limits_colimits/MonoidalLimits.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Products.jl b/src/categorical_algebra/cats/limits_colimits/Products.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Products.jl
rename to src/categorical_algebra/cats/limits_colimits/Products.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Pullbacks.jl b/src/categorical_algebra/cats/limits_colimits/Pullbacks.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Pullbacks.jl
rename to src/categorical_algebra/cats/limits_colimits/Pullbacks.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Pushouts.jl b/src/categorical_algebra/cats/limits_colimits/Pushouts.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Pushouts.jl
rename to src/categorical_algebra/cats/limits_colimits/Pushouts.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Singletons.jl b/src/categorical_algebra/cats/limits_colimits/Singletons.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Singletons.jl
rename to src/categorical_algebra/cats/limits_colimits/Singletons.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/Terminals.jl b/src/categorical_algebra/cats/limits_colimits/Terminals.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/Terminals.jl
rename to src/categorical_algebra/cats/limits_colimits/Terminals.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/module.jl b/src/categorical_algebra/cats/limits_colimits/module.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/module.jl
rename to src/categorical_algebra/cats/limits_colimits/module.jl
diff --git a/src/04_categorical_algebra/01_cats/09_limits_colimits/other_limits/TrivialLimits.jl b/src/categorical_algebra/cats/limits_colimits/other_limits/TrivialLimits.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/09_limits_colimits/other_limits/TrivialLimits.jl
rename to src/categorical_algebra/cats/limits_colimits/other_limits/TrivialLimits.jl
diff --git a/src/categorical_algebra/cats/module.jl b/src/categorical_algebra/cats/module.jl
new file mode 100644
index 000000000..c76e3d93f
--- /dev/null
+++ b/src/categorical_algebra/cats/module.jl
@@ -0,0 +1,44 @@
+module Cats 
+
+using Reexport
+
+include("paths/Paths.jl") # [DEPS]
+@reexport using .Paths
+
+include("categories/module.jl") #
+@reexport using .Categories
+
+include("fincats/module.jl") # 2
+@reexport using .FinCats
+
+include("functors/module.jl") # 2
+@reexport using .Functors
+
+include("freediagrams/module.jl") # 3
+@reexport using .FreeDiagrams
+
+include("finfunctors/module.jl") # 2, 5
+@reexport using .FinFunctors
+
+include("cat_of_cat/CatOfCat.jl") # 2
+@reexport using .CatOfCat
+
+include("natural_transformations/module.jl")
+@reexport using .Transformations
+
+include("limits_colimits/module.jl") # 4,5
+@reexport using .LimitsColimits
+
+include("commutative_diagrams/CommutativeDiagrams.jl")
+@reexport using .CommutativeDiagrams
+
+include("diagrams/module.jl") # 5
+@reexport using .Diagrams
+
+include("slice/module.jl")
+@reexport using .SliceCategories
+
+include("subobjects/Subobjects.jl") # Limits
+@reexport using .Subobjects
+
+end # module
diff --git a/src/04_categorical_algebra/01_cats/08_natural_transformations/IdTrans.jl b/src/categorical_algebra/cats/natural_transformations/IdTrans.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/08_natural_transformations/IdTrans.jl
rename to src/categorical_algebra/cats/natural_transformations/IdTrans.jl
diff --git a/src/04_categorical_algebra/01_cats/08_natural_transformations/MapTrans.jl b/src/categorical_algebra/cats/natural_transformations/MapTrans.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/08_natural_transformations/MapTrans.jl
rename to src/categorical_algebra/cats/natural_transformations/MapTrans.jl
diff --git a/src/04_categorical_algebra/01_cats/08_natural_transformations/OpTrans.jl b/src/categorical_algebra/cats/natural_transformations/OpTrans.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/08_natural_transformations/OpTrans.jl
rename to src/categorical_algebra/cats/natural_transformations/OpTrans.jl
diff --git a/src/04_categorical_algebra/01_cats/08_natural_transformations/Transformations.jl b/src/categorical_algebra/cats/natural_transformations/Transformations.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/08_natural_transformations/Transformations.jl
rename to src/categorical_algebra/cats/natural_transformations/Transformations.jl
diff --git a/src/04_categorical_algebra/01_cats/08_natural_transformations/TwoCat.jl b/src/categorical_algebra/cats/natural_transformations/TwoCat.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/08_natural_transformations/TwoCat.jl
rename to src/categorical_algebra/cats/natural_transformations/TwoCat.jl
diff --git a/src/04_categorical_algebra/01_cats/08_natural_transformations/module.jl b/src/categorical_algebra/cats/natural_transformations/module.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/08_natural_transformations/module.jl
rename to src/categorical_algebra/cats/natural_transformations/module.jl
diff --git a/src/04_categorical_algebra/01_cats/01_paths/Paths.jl b/src/categorical_algebra/cats/paths/Paths.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/01_paths/Paths.jl
rename to src/categorical_algebra/cats/paths/Paths.jl
diff --git a/src/04_categorical_algebra/01_cats/12_slice/LimitsColimits.jl b/src/categorical_algebra/cats/slice/LimitsColimits.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/12_slice/LimitsColimits.jl
rename to src/categorical_algebra/cats/slice/LimitsColimits.jl
diff --git a/src/04_categorical_algebra/01_cats/12_slice/SliceCategories.jl b/src/categorical_algebra/cats/slice/SliceCategories.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/12_slice/SliceCategories.jl
rename to src/categorical_algebra/cats/slice/SliceCategories.jl
diff --git a/src/04_categorical_algebra/01_cats/12_slice/module.jl b/src/categorical_algebra/cats/slice/module.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/12_slice/module.jl
rename to src/categorical_algebra/cats/slice/module.jl
diff --git a/src/04_categorical_algebra/01_cats/13_subobjects/Subobjects.jl b/src/categorical_algebra/cats/subobjects/Subobjects.jl
similarity index 100%
rename from src/04_categorical_algebra/01_cats/13_subobjects/Subobjects.jl
rename to src/categorical_algebra/cats/subobjects/Subobjects.jl
diff --git a/src/04_categorical_algebra/04_misc/FinRelations.jl b/src/categorical_algebra/misc/FinRelations.jl
similarity index 100%
rename from src/04_categorical_algebra/04_misc/FinRelations.jl
rename to src/categorical_algebra/misc/FinRelations.jl
diff --git a/src/04_categorical_algebra/04_misc/Matrices.jl b/src/categorical_algebra/misc/Matrices.jl
similarity index 100%
rename from src/04_categorical_algebra/04_misc/Matrices.jl
rename to src/categorical_algebra/misc/Matrices.jl
diff --git a/src/04_categorical_algebra/04_misc/Permutations.jl b/src/categorical_algebra/misc/Permutations.jl
similarity index 100%
rename from src/04_categorical_algebra/04_misc/Permutations.jl
rename to src/categorical_algebra/misc/Permutations.jl
diff --git a/src/04_categorical_algebra/04_misc/module.jl b/src/categorical_algebra/misc/module.jl
similarity index 100%
rename from src/04_categorical_algebra/04_misc/module.jl
rename to src/categorical_algebra/misc/module.jl
diff --git a/src/categorical_algebra/module.jl b/src/categorical_algebra/module.jl
new file mode 100644
index 000000000..cc82cb39d
--- /dev/null
+++ b/src/categorical_algebra/module.jl
@@ -0,0 +1,18 @@
+module CategoricalAlgebra
+
+using Reexport
+
+include("cats/module.jl") 
+@reexport using .Cats
+
+include("setcats/module.jl") # depends on Cats
+@reexport using .SetCats
+
+include("pointwise/module.jl") # depends on Cats, SetCats
+@reexport using .Pointwise
+
+include("misc/module.jl") # doesn't depend on the other three
+
+@reexport using .Misc
+
+end # module
diff --git a/src/04_categorical_algebra/03_pointwise/01_acsettransformations/ACSetTransformations.jl b/src/categorical_algebra/pointwise/acsettransformations/ACSetTransformations.jl
similarity index 94%
rename from src/04_categorical_algebra/03_pointwise/01_acsettransformations/ACSetTransformations.jl
rename to src/categorical_algebra/pointwise/acsettransformations/ACSetTransformations.jl
index d674ae8dd..16e84d3bf 100644
--- a/src/04_categorical_algebra/03_pointwise/01_acsettransformations/ACSetTransformations.jl
+++ b/src/categorical_algebra/pointwise/acsettransformations/ACSetTransformations.jl
@@ -142,14 +142,9 @@ end
 
 # WARNING that this means :cat is a reserved name for schema entities.
 """Move components as first argument"""
-ACSetTransformation(X::ACSet, Y::ACSet; cat=nothing, components...) =
+function ACSetTransformation(X::ACSet, Y::ACSet; cat=nothing, components...)
   ACSetTransformation((; components...), X, Y; cat)
-      
-# ACSetTransformation(components, X::StructACSet{S}, Y::StructACSet{S}) where {S} = 
-#   _ACSetTransformation(Val{S},components,X,Y,Val{true})
-
-# ACSetTransformation(components, X::DynamicACSet, Y::DynamicACSet) = 
-#   runtime(_ACSetTransformation, X.schema, components, X,Y,false)
+end
 
 function _ACSetTransformation(components, X::StructACSet{S}, Y::StructACSet{S}
                              ) where S
diff --git a/src/04_categorical_algebra/03_pointwise/06_catelements/CatElements.jl b/src/categorical_algebra/pointwise/catelements/CatElements.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/06_catelements/CatElements.jl
rename to src/categorical_algebra/pointwise/catelements/CatElements.jl
diff --git a/src/04_categorical_algebra/03_pointwise/08_chase/Chase.jl b/src/categorical_algebra/pointwise/chase/Chase.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/08_chase/Chase.jl
rename to src/categorical_algebra/pointwise/chase/Chase.jl
diff --git a/src/04_categorical_algebra/03_pointwise/02_csets/ACSetFunctors.jl b/src/categorical_algebra/pointwise/csets/ACSetFunctors.jl
similarity index 90%
rename from src/04_categorical_algebra/03_pointwise/02_csets/ACSetFunctors.jl
rename to src/categorical_algebra/pointwise/csets/ACSetFunctors.jl
index f3a0bffdd..512bcc4c3 100644
--- a/src/04_categorical_algebra/03_pointwise/02_csets/ACSetFunctors.jl
+++ b/src/categorical_algebra/pointwise/csets/ACSetFunctors.jl
@@ -60,20 +60,13 @@ FinDomFunctor(acs::ACSet; cat=nothing) =
 ###########################################
 
 
-# Set-valued FinDomFunctors as ACSets.
+""" Set-valued FinDomFunctors as ACSets. """
 function (::Type{ACS})(F::FinDomFunctor) where ACS <: ACSet
   getvalue(F) isa ACSetFunctor && return getvalue(F).acset
-  X = if ACS isa UnionAll
-    pres = presentation(dom(F))
-    ACS{(strip_attrvars(eltype(ob_map(F, c))) for c in generators(pres, :AttrType))...}()
-  else
-    ACS()
-  end
+  X = ACS()
   copy_parts!(X, F)
   return X
 end
-strip_attrvars(T) = T
-strip_attrvars(::Type{Union{AttrVar, T}}) where T = T
 
 """ Copy parts from a set-valued `FinDomFunctor` to an `ACSet`.
 """
diff --git a/src/04_categorical_algebra/03_pointwise/02_csets/CSets.jl b/src/categorical_algebra/pointwise/csets/CSets.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/02_csets/CSets.jl
rename to src/categorical_algebra/pointwise/csets/CSets.jl
diff --git a/src/04_categorical_algebra/03_pointwise/02_csets/CollageCats.jl b/src/categorical_algebra/pointwise/csets/CollageCats.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/02_csets/CollageCats.jl
rename to src/categorical_algebra/pointwise/csets/CollageCats.jl
diff --git a/src/04_categorical_algebra/03_pointwise/02_csets/Heteromorphisms.jl b/src/categorical_algebra/pointwise/csets/Heteromorphisms.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/02_csets/Heteromorphisms.jl
rename to src/categorical_algebra/pointwise/csets/Heteromorphisms.jl
diff --git a/src/04_categorical_algebra/03_pointwise/02_csets/module.jl b/src/categorical_algebra/pointwise/csets/module.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/02_csets/module.jl
rename to src/categorical_algebra/pointwise/csets/module.jl
diff --git a/src/04_categorical_algebra/03_pointwise/09_datamigrations/FunctorialDataMigrations.jl b/src/categorical_algebra/pointwise/datamigrations/FunctorialDataMigrations.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/09_datamigrations/FunctorialDataMigrations.jl
rename to src/categorical_algebra/pointwise/datamigrations/FunctorialDataMigrations.jl
diff --git a/src/04_categorical_algebra/03_pointwise/09_datamigrations/Yoneda.jl b/src/categorical_algebra/pointwise/datamigrations/Yoneda.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/09_datamigrations/Yoneda.jl
rename to src/categorical_algebra/pointwise/datamigrations/Yoneda.jl
diff --git a/src/04_categorical_algebra/03_pointwise/09_datamigrations/module.jl b/src/categorical_algebra/pointwise/datamigrations/module.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/09_datamigrations/module.jl
rename to src/categorical_algebra/pointwise/datamigrations/module.jl
diff --git a/src/04_categorical_algebra/03_pointwise/05_homsearch/HomSearch.jl b/src/categorical_algebra/pointwise/homsearch/HomSearch.jl
similarity index 99%
rename from src/04_categorical_algebra/03_pointwise/05_homsearch/HomSearch.jl
rename to src/categorical_algebra/pointwise/homsearch/HomSearch.jl
index 53a400ec3..d071f7e92 100644
--- a/src/04_categorical_algebra/03_pointwise/05_homsearch/HomSearch.jl
+++ b/src/categorical_algebra/pointwise/homsearch/HomSearch.jl
@@ -210,6 +210,7 @@ struct BacktrackingState{
   predicates::Predicates
   image::Image # Negative of image for epic components or if finding an epimorphism
   unassigned::Unassign # "# of unassigned elems in domain of a component 
+  cat::ACSetCategory
 end
 
 function backtracking_search(f, X::ACSet, Y::ACSet;
@@ -299,7 +300,7 @@ function backtracking_search(f, X::ACSet, Y::ACSet;
 
   state = BacktrackingState(assignment, assignment_depth, 
                             inv_assignment, X, Y, loosefuns, pred_nt,
-                            images, unassigned)
+                            images, unassigned, cat)
 
   # Make any initial assignments, failing immediately if inconsistent.
   for (c, c_assignments) in pairs(initial)
@@ -341,7 +342,7 @@ function backtracking_search(f, state::BacktrackingState, depth::Int;
         state.assignment, state.type_components, state.dom, state.codom)])
     else
       m = Dict(k=>!isnothing(v) for (k,v) in pairs(state.inv_assignment))
-      return f(postprocess_search_results(state.dom, state.codom, state.assignment, m))
+      return f(postprocess_search_results(state.dom, state.codom, state.assignment, m; cat=state.cat))
     end
   elseif mrv == 0
     # An element has no allowable assignment, so we must backtrack.
@@ -522,7 +523,7 @@ representables.
 This function takes a result assignment from backtracking search and returns an
 iterator of the implicit set of homomorphisms that it specifies.
 """
-function postprocess_search_results(dom, codom, assgn, monic)
+function postprocess_search_results(dom, codom, assgn, monic; cat)
   S = acset_schema(dom)
   od = Dict{Symbol,Vector{Int}}(k=>(assgn[k]) for k in objects(S))
 
@@ -547,7 +548,7 @@ function postprocess_search_results(dom, codom, assgn, monic)
       k => vec
     end)
     comps = merge(NamedTuple(od),NamedTuple(ad))
-    ACSetTransformation(comps, dom, codom)
+    ACSetTransformation(comps, dom, codom; cat)
   end
 end
 
diff --git a/src/04_categorical_algebra/03_pointwise/05_homsearch/MCO.jl b/src/categorical_algebra/pointwise/homsearch/MCO.jl
similarity index 95%
rename from src/04_categorical_algebra/03_pointwise/05_homsearch/MCO.jl
rename to src/categorical_algebra/pointwise/homsearch/MCO.jl
index 4e6b5686d..ebbf7ca83 100644
--- a/src/04_categorical_algebra/03_pointwise/05_homsearch/MCO.jl
+++ b/src/categorical_algebra/pointwise/homsearch/MCO.jl
@@ -79,10 +79,10 @@ end
 
 """This would be much more efficient with canonical isomorph"""
 function is_seen(cat, S::SubobjectIteratorState, f::ACSetTransformation)
-  for h in S.seen 
-    if any(σ -> force(compose[cat](σ,h); cat) == force(f; cat), 
-           isomorphisms(dom(f),dom(h)))
-      return true 
+  for h in S.seen
+    for σ in isomorphisms(dom(f),dom(h); cat) 
+      σ = force(σ; cat) # TODO this should be done automatically in homsearch 
+      force(compose[cat](σ,h); cat) == force(f; cat) && return true
     end
   end
   return false
@@ -261,8 +261,8 @@ these are all returned.
 If there are attributes, we ignore these and use variables in the apex of the 
 overlap.
 """
-function maximum_common_subobject(Xs::Vector{T}; abstract=true) where T <: ACSet
-  it = partial_overlaps(Xs; abstract)
+function maximum_common_subobject(Xs::Vector{T}; abstract=true, kw...) where T <: ACSet
+  it = partial_overlaps(Xs; abstract, kw...)
   osize = -1
   res = DefaultDict(()->[])
   for overlap in it 
@@ -275,7 +275,7 @@ function maximum_common_subobject(Xs::Vector{T}; abstract=true) where T <: ACSet
   return res
 end
 
-maximum_common_subobject(Xs::T...; abstract=true) where T <: ACSet = 
-  maximum_common_subobject(collect(Xs); abstract)
+maximum_common_subobject(Xs::ACSet...; abstract=true, kw...) = 
+  maximum_common_subobject(collect(Xs); abstract, kw...)
 
 end # module
\ No newline at end of file
diff --git a/src/04_categorical_algebra/03_pointwise/05_homsearch/VMSearch.jl b/src/categorical_algebra/pointwise/homsearch/VMSearch.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/05_homsearch/VMSearch.jl
rename to src/categorical_algebra/pointwise/homsearch/VMSearch.jl
diff --git a/src/04_categorical_algebra/03_pointwise/05_homsearch/module.jl b/src/categorical_algebra/pointwise/homsearch/module.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/05_homsearch/module.jl
rename to src/categorical_algebra/pointwise/homsearch/module.jl
diff --git a/src/04_categorical_algebra/03_pointwise/04_limits_colimits/Colimits.jl b/src/categorical_algebra/pointwise/limits_colimits/Colimits.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/04_limits_colimits/Colimits.jl
rename to src/categorical_algebra/pointwise/limits_colimits/Colimits.jl
diff --git a/src/04_categorical_algebra/03_pointwise/04_limits_colimits/Limits.jl b/src/categorical_algebra/pointwise/limits_colimits/Limits.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/04_limits_colimits/Limits.jl
rename to src/categorical_algebra/pointwise/limits_colimits/Limits.jl
diff --git a/src/04_categorical_algebra/03_pointwise/04_limits_colimits/LimitsColimits.jl b/src/categorical_algebra/pointwise/limits_colimits/LimitsColimits.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/04_limits_colimits/LimitsColimits.jl
rename to src/categorical_algebra/pointwise/limits_colimits/LimitsColimits.jl
diff --git a/src/04_categorical_algebra/03_pointwise/04_limits_colimits/module.jl b/src/categorical_algebra/pointwise/limits_colimits/module.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/04_limits_colimits/module.jl
rename to src/categorical_algebra/pointwise/limits_colimits/module.jl
diff --git a/src/categorical_algebra/pointwise/module.jl b/src/categorical_algebra/pointwise/module.jl
new file mode 100644
index 000000000..deb40b964
--- /dev/null
+++ b/src/categorical_algebra/pointwise/module.jl
@@ -0,0 +1,34 @@
+module Pointwise 
+using Reexport
+
+include("acsettransformations/ACSetTransformations.jl")
+@reexport using .ACSetTransformations
+
+include("csets/module.jl")
+@reexport using .CSets
+
+include("pointwisecats/module.jl")
+@reexport using .PointwiseCats
+
+include("limits_colimits/module.jl")
+@reexport using .LimitsColimits
+
+include("homsearch/module.jl")
+@reexport using .HomSearch
+
+include("catelements/CatElements.jl")
+@reexport using .CatElements
+
+include("subcsets/SubCSets.jl")
+@reexport using .SubCSets
+
+include("chase/Chase.jl")
+@reexport using .Chase
+
+include("datamigrations/module.jl")
+@reexport using .FunctorialDataMigrations
+
+include("structured_cospans/StructuredCospans.jl")
+@reexport using .StructuredCospans
+
+end # module
diff --git a/src/04_categorical_algebra/03_pointwise/03_pointwisecats/ACSetCats.jl b/src/categorical_algebra/pointwise/pointwisecats/ACSetCats.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/03_pointwisecats/ACSetCats.jl
rename to src/categorical_algebra/pointwise/pointwisecats/ACSetCats.jl
diff --git a/src/04_categorical_algebra/03_pointwise/03_pointwisecats/ACSetLooseCats.jl b/src/categorical_algebra/pointwise/pointwisecats/ACSetLooseCats.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/03_pointwisecats/ACSetLooseCats.jl
rename to src/categorical_algebra/pointwise/pointwisecats/ACSetLooseCats.jl
diff --git a/src/04_categorical_algebra/03_pointwise/03_pointwisecats/CParCats.jl b/src/categorical_algebra/pointwise/pointwisecats/CParCats.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/03_pointwisecats/CParCats.jl
rename to src/categorical_algebra/pointwise/pointwisecats/CParCats.jl
diff --git a/src/04_categorical_algebra/03_pointwise/03_pointwisecats/CSetCats.jl b/src/categorical_algebra/pointwise/pointwisecats/CSetCats.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/03_pointwisecats/CSetCats.jl
rename to src/categorical_algebra/pointwise/pointwisecats/CSetCats.jl
diff --git a/src/04_categorical_algebra/03_pointwise/03_pointwisecats/CatsOfACSet.jl b/src/categorical_algebra/pointwise/pointwisecats/CatsOfACSet.jl
similarity index 94%
rename from src/04_categorical_algebra/03_pointwise/03_pointwisecats/CatsOfACSet.jl
rename to src/categorical_algebra/pointwise/pointwisecats/CatsOfACSet.jl
index 35b6a3692..6b9eed594 100644
--- a/src/04_categorical_algebra/03_pointwise/03_pointwisecats/CatsOfACSet.jl
+++ b/src/categorical_algebra/pointwise/pointwisecats/CatsOfACSet.jl
@@ -30,6 +30,7 @@ using ...CSets
 
   function compose(f::ACSetTransformation, g::ACSetTransformation)
     S = acset_schema(model)
+    f, g = coerce(f; cat=model), coerce(g; cat=model) # we shouldn't have to do this
     𝒞, 𝒟 = Category(entity_cat(model)), t->Category(attr_cat(model,t))
     ecomps = Dict(o => compose(𝒞, f[o], g[o]) for o in ob(S))
     acomps = Dict(o => compose(𝒟(o), f[o], g[o]) for o in attrtypes(S))
diff --git a/src/04_categorical_algebra/03_pointwise/03_pointwisecats/InferCat.jl b/src/categorical_algebra/pointwise/pointwisecats/InferCat.jl
similarity index 97%
rename from src/04_categorical_algebra/03_pointwise/03_pointwisecats/InferCat.jl
rename to src/categorical_algebra/pointwise/pointwisecats/InferCat.jl
index 80e268e5a..5557b8472 100644
--- a/src/04_categorical_algebra/03_pointwise/03_pointwisecats/InferCat.jl
+++ b/src/categorical_algebra/pointwise/pointwisecats/InferCat.jl
@@ -33,12 +33,12 @@ function infer_acset_cat(X::ACSet)::ACSetCategory
   return ACSetCategory(cat(X))
 end
 
-
-function hasvar(X::ACSet,x) 
+function hasvar(X::ACSet, x)
   s = acset_schema(X)
   (x∈ attrs(acset_schema(X),just_names=true) && hasvar(X,codom(s,x))) || 
   x∈attrtypes(acset_schema(X)) && nparts(X,x)>0
 end
+
 hasvar(X::ACSet) = any(o->hasvar(X,o), attrtypes(acset_schema(X)))
   
 function ACSetTransformation(comps, dom::ACSet, codom::ACSet; 
diff --git a/src/04_categorical_algebra/03_pointwise/03_pointwisecats/VarACSetCats.jl b/src/categorical_algebra/pointwise/pointwisecats/VarACSetCats.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/03_pointwisecats/VarACSetCats.jl
rename to src/categorical_algebra/pointwise/pointwisecats/VarACSetCats.jl
diff --git a/src/04_categorical_algebra/03_pointwise/03_pointwisecats/module.jl b/src/categorical_algebra/pointwise/pointwisecats/module.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/03_pointwisecats/module.jl
rename to src/categorical_algebra/pointwise/pointwisecats/module.jl
diff --git a/src/04_categorical_algebra/03_pointwise/10_structured_cospans/StructuredCospans.jl b/src/categorical_algebra/pointwise/structured_cospans/StructuredCospans.jl
similarity index 100%
rename from src/04_categorical_algebra/03_pointwise/10_structured_cospans/StructuredCospans.jl
rename to src/categorical_algebra/pointwise/structured_cospans/StructuredCospans.jl
diff --git a/src/04_categorical_algebra/03_pointwise/07_subcsets/SubCSets.jl b/src/categorical_algebra/pointwise/subcsets/SubCSets.jl
similarity index 88%
rename from src/04_categorical_algebra/03_pointwise/07_subcsets/SubCSets.jl
rename to src/categorical_algebra/pointwise/subcsets/SubCSets.jl
index 386d52e95..c1dedbeb2 100644
--- a/src/04_categorical_algebra/03_pointwise/07_subcsets/SubCSets.jl
+++ b/src/categorical_algebra/pointwise/subcsets/SubCSets.jl
@@ -9,7 +9,7 @@ using ACSets, GATlab
 import .....Theories: ob, hom, top, bottom, meet, join
 
 using .....BasicSets, ...Cats, ...SetCats
-import .....BasicSets: preimage
+import .....BasicSets: preimage, left
 import ...Cats: components, implies, subtract, negate, non, force
 using ..Pointwise
 
@@ -18,15 +18,31 @@ using Base.Meta: quot
 # Sub-C-sets
 ############
 
+""" assume a VarFunction is secretly a FinFunction """
+function left(f::FinDomFunction)::FinFunction
+  get_left(l::Left) = getvalue(l)
+  get_left(r::Right) = error(
+    "Tried to coerce VarFunction $f to FinFunction, got value $r")
+  lft = SetFunction(SetFunctionCallable(get_left, codom(f), 
+                    left(getvalue(codom(f)))))
+  force(compose[SetC()](f, lft))
+end
+
 """ Sub-C-set of a C-set.
 """
 const SubACSet{S} = Subobject{<:StructACSet{S}}
 
-# Componentwise subobjects: coerce VarFunctions to FinFunctions
-components(A::SubACSet{S}) where S = 
-  NamedTuple(k => Subobject(k ∈ ob(S) ? vs : FinFunction(vs)) for (k,vs) in 
-             pairs(components(hom(A)))
-)
+""" 
+Componentwise subobjects: note we must coerce VarFunctions (which only make 
+reference to AttrVars) into FinFunctions 
+"""
+function components(A::SubACSet{S}) where S 
+  𝒞 = infer_acset_cat(ob(A))
+  FF = getvalue(𝒞) isa CSetCat ? FinFunction : left
+  NamedTuple(sort(map(collect(pairs(components(hom(A))))) do (k,vs) 
+    k => Subobject(k ∈ ob(S) ? vs : FF(vs))
+  end; by=first))
+end
 
 force(A::SubACSet) = Subobject(force(hom(A)))
 
@@ -41,7 +57,8 @@ force(A::SubACSet) = Subobject(force(hom(A)))
     S = acset_schema(X)
     cat = isnothing(cat) ? infer_acset_cat(X) : cat
     X_sets = NamedTuple(c => FinSet(get_ob(cat,X,c)) for c in types(S))
-    @assert keys(components) ⊆ keys(X_sets)
+    keys(components) ⊆ keys(X_sets) || error(
+      "$(keys(components)) ⊈ $(keys(X_sets))")
     coerced_components = NamedTuple{keys(X_sets)}(
       coerce_subob_component(set, get(components, ob, 1:0))
       for (ob, set) in pairs(X_sets))
@@ -65,7 +82,8 @@ end
 coerce_subob_component(X::FinSet, f) = Subobject(X, f)
 
 ob(A::SubACSetComponentwise) = A.ob
-components(A::SubACSetComponentwise) = A.components
+components(A::SubACSetComponentwise) = NamedTuple(sort(collect(
+  pairs(A.components)); by=first))
 
 function hom(A::SubACSetComponentwise{T}) where T <: ACSet
   X = ob(A)
diff --git a/src/04_categorical_algebra/02_setcats/CatsInterop.jl b/src/categorical_algebra/setcats/CatsInterop.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/CatsInterop.jl
rename to src/categorical_algebra/setcats/CatsInterop.jl
diff --git a/src/04_categorical_algebra/02_setcats/DiscreteCatLimits.jl b/src/categorical_algebra/setcats/DiscreteCatLimits.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/DiscreteCatLimits.jl
rename to src/categorical_algebra/setcats/DiscreteCatLimits.jl
diff --git a/src/04_categorical_algebra/02_setcats/FinSetCat/Colimits.jl b/src/categorical_algebra/setcats/FinSetCat/Colimits.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/FinSetCat/Colimits.jl
rename to src/categorical_algebra/setcats/FinSetCat/Colimits.jl
diff --git a/src/04_categorical_algebra/02_setcats/FinSetCat/FinSetCat.jl b/src/categorical_algebra/setcats/FinSetCat/FinSetCat.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/FinSetCat/FinSetCat.jl
rename to src/categorical_algebra/setcats/FinSetCat/FinSetCat.jl
diff --git a/src/04_categorical_algebra/02_setcats/FinSetCat/Limits.jl b/src/categorical_algebra/setcats/FinSetCat/Limits.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/FinSetCat/Limits.jl
rename to src/categorical_algebra/setcats/FinSetCat/Limits.jl
diff --git a/src/04_categorical_algebra/02_setcats/FinSetCat/module.jl b/src/categorical_algebra/setcats/FinSetCat/module.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/FinSetCat/module.jl
rename to src/categorical_algebra/setcats/FinSetCat/module.jl
diff --git a/src/04_categorical_algebra/02_setcats/GraphCategories.jl b/src/categorical_algebra/setcats/GraphCategories.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/GraphCategories.jl
rename to src/categorical_algebra/setcats/GraphCategories.jl
diff --git a/src/04_categorical_algebra/02_setcats/SetCat/Colimits.jl b/src/categorical_algebra/setcats/SetCat/Colimits.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/SetCat/Colimits.jl
rename to src/categorical_algebra/setcats/SetCat/Colimits.jl
diff --git a/src/04_categorical_algebra/02_setcats/SetCat/Limits.jl b/src/categorical_algebra/setcats/SetCat/Limits.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/SetCat/Limits.jl
rename to src/categorical_algebra/setcats/SetCat/Limits.jl
diff --git a/src/04_categorical_algebra/02_setcats/SetCat/SetCat.jl b/src/categorical_algebra/setcats/SetCat/SetCat.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/SetCat/SetCat.jl
rename to src/categorical_algebra/setcats/SetCat/SetCat.jl
diff --git a/src/04_categorical_algebra/02_setcats/SetCat/module.jl b/src/categorical_algebra/setcats/SetCat/module.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/SetCat/module.jl
rename to src/categorical_algebra/setcats/SetCat/module.jl
diff --git a/src/04_categorical_algebra/02_setcats/SkelFinSetCat/Colimits.jl b/src/categorical_algebra/setcats/SkelFinSetCat/Colimits.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/SkelFinSetCat/Colimits.jl
rename to src/categorical_algebra/setcats/SkelFinSetCat/Colimits.jl
diff --git a/src/04_categorical_algebra/02_setcats/SkelFinSetCat/Limits.jl b/src/categorical_algebra/setcats/SkelFinSetCat/Limits.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/SkelFinSetCat/Limits.jl
rename to src/categorical_algebra/setcats/SkelFinSetCat/Limits.jl
diff --git a/src/04_categorical_algebra/02_setcats/SkelFinSetCat/SkelFinSetCat.jl b/src/categorical_algebra/setcats/SkelFinSetCat/SkelFinSetCat.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/SkelFinSetCat/SkelFinSetCat.jl
rename to src/categorical_algebra/setcats/SkelFinSetCat/SkelFinSetCat.jl
diff --git a/src/04_categorical_algebra/02_setcats/SkelFinSetCat/module.jl b/src/categorical_algebra/setcats/SkelFinSetCat/module.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/SkelFinSetCat/module.jl
rename to src/categorical_algebra/setcats/SkelFinSetCat/module.jl
diff --git a/src/04_categorical_algebra/02_setcats/Subsets.jl b/src/categorical_algebra/setcats/Subsets.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/Subsets.jl
rename to src/categorical_algebra/setcats/Subsets.jl
diff --git a/src/04_categorical_algebra/02_setcats/VarFunctions/SkelVarFnCat.jl b/src/categorical_algebra/setcats/VarFunctions/SkelVarFnCat.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/VarFunctions/SkelVarFnCat.jl
rename to src/categorical_algebra/setcats/VarFunctions/SkelVarFnCat.jl
diff --git a/src/04_categorical_algebra/02_setcats/VarFunctions/VarFnLimits.jl b/src/categorical_algebra/setcats/VarFunctions/VarFnLimits.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/VarFunctions/VarFnLimits.jl
rename to src/categorical_algebra/setcats/VarFunctions/VarFnLimits.jl
diff --git a/src/04_categorical_algebra/02_setcats/VarFunctions/module.jl b/src/categorical_algebra/setcats/VarFunctions/module.jl
similarity index 100%
rename from src/04_categorical_algebra/02_setcats/VarFunctions/module.jl
rename to src/categorical_algebra/setcats/VarFunctions/module.jl
diff --git a/src/04_categorical_algebra/02_setcats/module.jl b/src/categorical_algebra/setcats/module.jl
similarity index 77%
rename from src/04_categorical_algebra/02_setcats/module.jl
rename to src/categorical_algebra/setcats/module.jl
index 19ef6991c..c625966c5 100644
--- a/src/04_categorical_algebra/02_setcats/module.jl
+++ b/src/categorical_algebra/setcats/module.jl
@@ -8,11 +8,6 @@ include("SkelFinSetCat/module.jl")
 include("FinSetCat/module.jl") 
 @reexport using .FinSetCat
 
-# This category doesn't make sense: no id morphisms on the non-finite sets.
-# include("FinDomSetCat/module.jl") 
-# @reexport using .FinDomSetCat
-
-
 include("SetCat/module.jl") 
 @reexport using .SetCat
 
@@ -22,11 +17,11 @@ include("CatsInterop.jl")
 include("Subsets.jl") 
 @reexport using .Subsets
 
+include("VarFunctions/module.jl")
+@reexport using .VarFunctions
+
 include("GraphCategories.jl") # (not reexported)
 
 include("DiscreteCatLimits.jl") # nothing to reexport
 
-include("VarFunctions/module.jl")
-@reexport using .VarFunctions
-
 end # module
diff --git a/src/02_graphs/BasicGraphs.jl b/src/graphs/BasicGraphs.jl
similarity index 100%
rename from src/02_graphs/BasicGraphs.jl
rename to src/graphs/BasicGraphs.jl
diff --git a/src/02_graphs/BipartiteGraphs.jl b/src/graphs/BipartiteGraphs.jl
similarity index 100%
rename from src/02_graphs/BipartiteGraphs.jl
rename to src/graphs/BipartiteGraphs.jl
diff --git a/src/02_graphs/GraphAlgorithms.jl b/src/graphs/GraphAlgorithms.jl
similarity index 100%
rename from src/02_graphs/GraphAlgorithms.jl
rename to src/graphs/GraphAlgorithms.jl
diff --git a/src/02_graphs/GraphGenerators.jl b/src/graphs/GraphGenerators.jl
similarity index 100%
rename from src/02_graphs/GraphGenerators.jl
rename to src/graphs/GraphGenerators.jl
diff --git a/src/02_graphs/GraphSearching.jl b/src/graphs/GraphSearching.jl
similarity index 100%
rename from src/02_graphs/GraphSearching.jl
rename to src/graphs/GraphSearching.jl
diff --git a/src/02_graphs/Graphs.jl b/src/graphs/Graphs.jl
similarity index 100%
rename from src/02_graphs/Graphs.jl
rename to src/graphs/Graphs.jl
diff --git a/src/02_graphs/NamedGraphs.jl b/src/graphs/NamedGraphs.jl
similarity index 100%
rename from src/02_graphs/NamedGraphs.jl
rename to src/graphs/NamedGraphs.jl
diff --git a/src/02_graphs/PropertyGraphs.jl b/src/graphs/PropertyGraphs.jl
similarity index 100%
rename from src/02_graphs/PropertyGraphs.jl
rename to src/graphs/PropertyGraphs.jl
diff --git a/src/01_theories/Category.jl b/src/theories/Category.jl
similarity index 100%
rename from src/01_theories/Category.jl
rename to src/theories/Category.jl
diff --git a/src/01_theories/HigherCategory.jl b/src/theories/HigherCategory.jl
similarity index 100%
rename from src/01_theories/HigherCategory.jl
rename to src/theories/HigherCategory.jl
diff --git a/src/01_theories/IndexedCategory.jl b/src/theories/IndexedCategory.jl
similarity index 100%
rename from src/01_theories/IndexedCategory.jl
rename to src/theories/IndexedCategory.jl
diff --git a/src/01_theories/Limits.jl b/src/theories/Limits.jl
similarity index 100%
rename from src/01_theories/Limits.jl
rename to src/theories/Limits.jl
diff --git a/src/01_theories/Monoidal.jl b/src/theories/Monoidal.jl
similarity index 100%
rename from src/01_theories/Monoidal.jl
rename to src/theories/Monoidal.jl
diff --git a/src/01_theories/MonoidalAdditive.jl b/src/theories/MonoidalAdditive.jl
similarity index 100%
rename from src/01_theories/MonoidalAdditive.jl
rename to src/theories/MonoidalAdditive.jl
diff --git a/src/01_theories/MonoidalMultiple.jl b/src/theories/MonoidalMultiple.jl
similarity index 100%
rename from src/01_theories/MonoidalMultiple.jl
rename to src/theories/MonoidalMultiple.jl
diff --git a/src/01_theories/Preorders.jl b/src/theories/Preorders.jl
similarity index 100%
rename from src/01_theories/Preorders.jl
rename to src/theories/Preorders.jl
diff --git a/src/01_theories/Relations.jl b/src/theories/Relations.jl
similarity index 100%
rename from src/01_theories/Relations.jl
rename to src/theories/Relations.jl
diff --git a/src/01_theories/Schema.jl b/src/theories/Schema.jl
similarity index 97%
rename from src/01_theories/Schema.jl
rename to src/theories/Schema.jl
index 7487c8e6b..d2073c9fc 100644
--- a/src/01_theories/Schema.jl
+++ b/src/theories/Schema.jl
@@ -4,6 +4,7 @@ export ThSchema, FreeSchema, AttrType, Attr, SchemaExpr, AttrTypeExpr, AttrExpr,
 ########
 
 # Why is ThSchema in Catlab rather than in GATlab?
+# TODO make this an optional dependency of ACSets
 
 """ The GAT that parameterizes Attributed C-sets
 A schema is comprised of a category C, a discrete category D, and a profunctor
diff --git a/src/01_theories/module.jl b/src/theories/module.jl
similarity index 100%
rename from src/01_theories/module.jl
rename to src/theories/module.jl
diff --git a/test/Project.toml b/test/Project.toml
index 79180e3ea..849bf4961 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,7 +1,6 @@
 [deps]
 ACSets = "227ef7b5-1206-438b-ac65-934d6da304b8"
 AlgebraicInterfaces = "23cfdc9f-0504-424a-be1f-4892b28e2f0c"
-Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
 Compose = "a81c6b42-2e10-5240-aca2-a61377ecd94b"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
diff --git a/test/aqua.jl b/test/aqua.jl
deleted file mode 100644
index f01188e8f..000000000
--- a/test/aqua.jl
+++ /dev/null
@@ -1,3 +0,0 @@
-using Aqua, Catlab 
-
-Aqua.test_all(Catlab, undefined_exports=false, project_extras=false, ambiguities=false) 
diff --git a/test/categorical_algebra/Pointwise/LabeledCSets/Limits.jl b/test/categorical_algebra/Pointwise/LabeledCSets/Limits.jl
index 10378f3ff..0b572ed9b 100644
--- a/test/categorical_algebra/Pointwise/LabeledCSets/Limits.jl
+++ b/test/categorical_algebra/Pointwise/LabeledCSets/Limits.jl
@@ -1,5 +1,41 @@
 module TestLabeledCSetLimits 
 
+using Catlab, Test
+
+const WG = WeightedGraph{Symbol}
+
+A = @acset WG begin 
+  V=1;E=2;Weight=1;src=1;tgt=1;weight=[AttrVar(1),:X] 
+end
+B = @acset WG begin V=1;E=2;Weight=1;src=1;tgt=1;weight=[:X, :Y] end
+
+𝒞 = infer_acset_cat(A)
+CM = TypedCatWithCoproducts(𝒞)
+C = @withmodel CM (⊕) begin
+  B ⊕ @acset WG begin V=1 end
+end
+
+
+AC = homomorphism(A,C; initial=(E=[1,1],))
+BC = CSetTransformation(B,C; V=[1],E=[1,2], Weight=[:X])
+@test all(is_natural,[AC,BC])
+p1, p2 = product(A,A; cset=true);
+X = @acset WG begin V=1;E=2;Weight=1;src=1;tgt=1;weight=[:X, :X] end
+@test nparts(apex(product(X,X;cset=true)),:Weight) == 1
+
+# Pullback in Graph from (Reyes et al 2004, p. 53), again
+g0, g1, g2 = WG.([2,3,2])
+add_edges!(g0, [1,1,2], [1,2,2]; weight=[:X,:Y,:Z])
+add_edges!(g1, [1,2,3], [2,3,3]; weight=[:Y,:Z,AttrVar(add_part!(g1,:Weight))])
+add_edges!(g2, [1,2,2], [1,2,2]; weight=[AttrVar(add_part!(g2,:Weight)), :Z,:Z])
+ϕ = homomorphism(g1, g0) |> CSetTransformation
+ψ = homomorphism(g2, g0; initial=(V=[1,2],)) |> CSetTransformation
+@test is_natural(ϕ) && is_natural(ψ)
+lim = pullback(ϕ, ψ)
+@test nv(ob(lim)) == 3
+@test sort!(collect(zip(src(ob(lim)), tgt(ob(lim))))) ==
+  [(2,3), (2,3), (3,3), (3,3)]
+@test is_natural(proj1(lim)) && is_natural(proj2(lim))
 # Example: "Reflexive graphs" where reflexive edges have weight -1
 A = @acset WeightedGraph{Float64} begin V=2; E=3; 
   src=[1, 2, 1]; tgt=[1, 2, 2]; weight=[-1, -1, 5] 
diff --git a/test/categorical_algebra/Pointwise/VarACSetCats/MCO.jl b/test/categorical_algebra/Pointwise/VarACSetCats/MCO.jl
index 471b297a9..e90e17916 100644
--- a/test/categorical_algebra/Pointwise/VarACSetCats/MCO.jl
+++ b/test/categorical_algebra/Pointwise/VarACSetCats/MCO.jl
@@ -6,9 +6,10 @@ using Catlab, Test
 #-----------------
 subG, subobjs = subobject_graph(path_graph(Graph, 3))
 
-
 G′ = path_graph(WeightedGraph{Bool}, 3)
 G′[:weight] = [false, AttrVar(add_part!(G′, :Weight))]
+
+𝒞 = infer_acset_cat(G′)
 subG′, subobjs′ = subobject_graph(G′)
 @test is_isomorphic(subG, subG′)
 @test nparts(dom(hom(first(subobjs′))), :Weight) == 1
@@ -34,7 +35,7 @@ end
 @acset_type VELabeledGraph(SchVELabeledGraph) <: AbstractGraph
 const LGraph = VELabeledGraph{Bool,Bool}
 
-G = @acset LGraph begin 
+G = @acset LGraph begin
   V=3; E=2; src=[1,2]; tgt=[2,3]; vlabel=Bool[0,1,1]; elabel=Bool[0,1]
 end
 H = @acset LGraph begin 
@@ -44,10 +45,10 @@ end
 𝒱 = ACSetCategory(VarACSetCat(LGraph()))
 os = partial_overlaps(G, H; cat=𝒱); # abstract=true
 @test count(apx->nparts(apx,:E)==2, apex.(os)) == 1
-os = partial_overlaps(G, H; abstract=[:VL]);
+os = collect(partial_overlaps(G, H; abstract=[:VL], cat=𝒱));
 @test count(apx->nparts(apx,:E)==2, apex.(os)) == 0
 @test count(apx->nparts(apx,:E)==1, apex.(os)) == 4
-os = partial_overlaps(G, H; abstract=false);
+os = partial_overlaps(G, H; abstract=false, cat=𝒱);
 @test count(apx->nparts(apx,:E)==2, apex.(os)) == 0
 @test count(apx->nparts(apx,:E)==1, apex.(os)) == 1
 
@@ -71,7 +72,7 @@ apex2 = @acset WG begin
   V=3; E=2; Weight=2; src=[1,3]; tgt=[2,3]; weight=AttrVar.(1:2)
 end
 
-results = collect(maximum_common_subobject(g1, g2))
+results = collect(maximum_common_subobject(g1, g2; cat=𝒞))
 @test length(results) == 2
 is_iso1 = map(result -> is_isomorphic(first(result), apex1), results)
 @test sum(is_iso1) == 1
@@ -90,4 +91,4 @@ results = first(is_iso1) ? results : reverse(results)
 exp = @acset WG begin V=3; E=1; src=1; tgt=2; weight=[false] end
 @test first(first(maximum_common_subobject(g1, g2; abstract=false))) == exp
 
-end # module
\ No newline at end of file
+end # module
diff --git a/test/categorical_algebra/Pointwise/VarACSetCats/MonoidalProducts.jl b/test/categorical_algebra/Pointwise/VarACSetCats/MonoidalProducts.jl
deleted file mode 100644
index 6934a793d..000000000
--- a/test/categorical_algebra/Pointwise/VarACSetCats/MonoidalProducts.jl
+++ /dev/null
@@ -1,26 +0,0 @@
-
-
-
-A = @acset WG{Symbol} begin V=1;E=2;Weight=1;src=1;tgt=1;weight=[AttrVar(1),:X] end
-B = @acset WG{Symbol} begin V=1;E=2;Weight=1;src=1;tgt=1;weight=[:X, :Y] end
-C = B ⊕ @acset WG{Symbol} begin V=1 end
-AC = homomorphism(A,C; initial=(E=[1,1],))
-BC = CSetTransformation(B,C; V=[1],E=[1,2], Weight=[:X])
-@test all(is_natural,[AC,BC])
-p1, p2 = product(A,A; cset=true);
-X = @acset WG{Symbol} begin V=1;E=2;Weight=1;src=1;tgt=1;weight=[:X, :X] end
-@test nparts(apex(product(X,X;cset=true)),:Weight) == 1
-
-# Pullback in Graph from (Reyes et al 2004, p. 53), again
-g0, g1, g2 = WG{Symbol}.([2,3,2])
-add_edges!(g0, [1,1,2], [1,2,2]; weight=[:X,:Y,:Z])
-add_edges!(g1, [1,2,3], [2,3,3]; weight=[:Y,:Z,AttrVar(add_part!(g1,:Weight))])
-add_edges!(g2, [1,2,2], [1,2,2]; weight=[AttrVar(add_part!(g2,:Weight)), :Z,:Z])
-ϕ = homomorphism(g1, g0) |> CSetTransformation
-ψ = homomorphism(g2, g0; initial=(V=[1,2],)) |> CSetTransformation
-@test is_natural(ϕ) && is_natural(ψ)
-lim = pullback(ϕ, ψ)
-@test nv(ob(lim)) == 3
-@test sort!(collect(zip(src(ob(lim)), tgt(ob(lim))))) ==
-  [(2,3), (2,3), (3,3), (3,3)]
-@test is_natural(proj1(lim)) && is_natural(proj2(lim))
\ No newline at end of file
diff --git a/test/categorical_algebra/Pointwise/VarACSetCats/Subobjects.jl b/test/categorical_algebra/Pointwise/VarACSetCats/Subobjects.jl
index 3539124a1..fd1b16a0b 100644
--- a/test/categorical_algebra/Pointwise/VarACSetCats/Subobjects.jl
+++ b/test/categorical_algebra/Pointwise/VarACSetCats/Subobjects.jl
@@ -2,15 +2,32 @@ module TestVarACSetSubobjects
 
 using Catlab, Test
 
+# SetAttr
+#########
+
 @present SchSetAttr(FreeSchema) begin X::Ob; D::AttrType; f::Attr(X,D) end
 @acset_type SetAttr(SchSetAttr)
 
 
 X = @acset SetAttr{Bool} begin X=2;D=1;f=[true, AttrVar(1)] end
+
+const 𝒞 = infer_acset_cat(X)
+
 A = Subobject(X, X=[1])
 B = Subobject(X, X=[2], D=[1])
-@test A ∧ B |> force == ⊥(X) |> force
-@test A ∨ B |> force == ⊤(X) |> force
+
+@withmodel 𝒞 (∧, ∨, ⊤, ⊥, bottom) begin 
+  @test A ∧ B |> force == ⊥(X) |> force
+  @test A ∨ B |> force == ⊤(X) |> force
+end
+
+
+# LabeledGraph
+###############
+@present SchVELabeledGraph <: SchGraph begin
+  Label::AttrType; vlabel::Attr(V,Label); elabel::Attr(E,Label)
+end
+@acset_type VELabeledGraph(SchVELabeledGraph,index=[:src,:tgt]) <: AbstractGraph
 
 const VES = VELabeledGraph{Symbol}
 
@@ -26,33 +43,58 @@ X = @acset VES begin V=6; E=5; Label=5
   vlabel=[:a,:b,:c,:d,:e,:f]; elabel=AttrVar.(1:5)
 end
 
+const 𝒟 = infer_acset_cat(X)
+
+
 A′ = Subobject(X, V=1:4, E=1:3, Label=1:3) # component-wise representation
 B′ = Subobject(X, V=3:6, E=3:5, Label=3:5)
 A′′, B′′ = Subobject.(hom.([A′,B′])) # hom representation
 
 for (A,B) in [A′=>B′, A′′ =>B′′]
-  @test A ∧ B |> force == Subobject(X, V=3:4, E=3:3, Label=3:3) |> force
-  expected = @acset VES begin V=2; E=1; Label=1;
-    src=1; tgt=2; vlabel=[:c,:d]; elabel=[AttrVar(1)]
-  end
-  @test is_isomorphic(dom(hom(A ∧ B )), expected)
-  @test A ∨ B |> force == Subobject(X, V=1:6, E=1:5, Label=1:5) |> force
-  @test ⊤(X) |> force == A ∨ B |> force
-  @test ⊥(X) |> force == Subobject(X, V=1:0, E=1:0, Label=1:0) |> force
-  @test force(implies(A, B)) == force(¬(A) ∨ B)
-  @test ¬(A ∧ B) == ¬(A) ∨ ¬(B)
-  @test ¬(A ∧ B) != ¬(A) ∨ B
-  @test (A ∧ implies(A,B)) == B ∧ (A ∧ implies(A,B))
-  @test (B ∧ implies(B,A)) == A ∧ (B ∧ implies(B,A))
-  @test ¬(A ∨ (¬B)) == ¬(A) ∧ ¬(¬(B))
-  @test ¬(A ∨ (¬B)) == ¬(A) ∧ B
-  @test A ∧ ¬(¬(A)) == ¬(¬(A))
-  @test implies((A∧B), A) == A∨B
-  @test dom(hom(subtract(A,B))) == @acset VES begin V=3; E=2; Label=2
-    src=[1,2]; tgt=3; vlabel=[:a,:b,:c]; elabel=AttrVar.(1:2)
-  end
+  @withmodel 𝒞 (∧, ∨,⊤, ⊥, ⟹, ¬, \, ~) begin #, subtract, implies, ~) begin 
+
+    # Conjunction
+    #------------
+    A_and_B = Subobject(X, V=3:4, E=3:3, Label=3:3) |> force
+    @test A ∧ B |> force == A_and_B    
+  
+    A_and_B_dom = @acset VES begin 
+      V=2; E=1; Label=1;
+      src=1; tgt=2; vlabel=[:c,:d]; elabel=[AttrVar(1)]
+    end  
+    @test is_isomorphic(dom(hom(A ∧ B )), A_and_B_dom)
+
+    # Disjunction
+    #------------
+
+    @test A ∨ B |> force == Subobject(X, V=1:6, E=1:5, Label=1:5) |> force
 
-  @test nv(dom(hom(~A))) == 3
+    # Top / bottom
+    #-------------
+    @test ⊤(X) |> force == A ∨ B |> force
+    @test ⊥(X) |> force == Subobject(X, V=1:0, E=1:0, Label=1:0) |> force
+
+    # Implication and not 
+    #--------------------
+    @test force(A⟹B) == force(¬(A) ∨ B)
+    @test ¬(A ∧ B) == ¬(A) ∨ ¬(B)
+    @test ¬(A ∧ B) != ¬(A) ∨ B
+    @test (A ∧ (A⟹B)) == B ∧ (A ∧ (A⟹B))
+    @test (B ∧ (B⟹A)) == A ∧ (B ∧ (B⟹A))
+    @test ¬(A ∨ (¬B)) == ¬(A) ∧ ¬(¬(B))
+    @test ¬(A ∨ (¬B)) == ¬(A) ∧ B
+    @test A ∧ ¬(¬(A)) == ¬(¬(A))
+    @test ((A∧B)⟹ A) == A∨B
+
+    AmB_dom = @acset VES begin 
+      V=3; E=2; Label=2
+      src=[1,2]; tgt=3; vlabel=[:a,:b,:c]; elabel=AttrVar.(1:2)
+    end
+
+    @test dom(hom(A\B)) == AmB_dom
+    @test nv(dom(hom(~A))) == 3
+  end
 end
 
+
 end # module
\ No newline at end of file
diff --git a/test/categorical_algebra/Pointwise/VarACSetCats/runtests.jl b/test/categorical_algebra/Pointwise/VarACSetCats/runtests.jl
index 9c6dff5be..170682f36 100644
--- a/test/categorical_algebra/Pointwise/VarACSetCats/runtests.jl
+++ b/test/categorical_algebra/Pointwise/VarACSetCats/runtests.jl
@@ -16,7 +16,9 @@ end
   include("DataMigrations.jl")
 end
 
-# include("Subobjects.jl")
-# include("MCO.jl")
-# include("MonoidalProducts.jl")
-
+@testset "Subobjects" begin
+  include("Subobjects.jl")
+end
+@testset "MCO" begin
+  include("MCO.jl")
+end