Merge pull request #461 from epatters/cset-subobjects

Function to create subobject of C-set

src/categorical_algebra/CSets.jl

@@ -2,7 +2,7 @@
 """
 module CSets
 export ACSetTransformation, CSetTransformation, components, force, is_natural,
-  homomorphism, homomorphisms, is_homomorphic,
+  subobject, homomorphism, homomorphisms, is_homomorphic,
   isomorphism, isomorphisms, is_isomorphic,
   generate_json_acset, parse_json_acset, read_json_acset, write_json_acset
 
@@ -156,6 +156,19 @@ map_components(f, α::ACSetTransformation) =
   ACSetTransformation(map(f, components(α)), dom(α), codom(α))
 force(α::ACSetTransformation) = map_components(force, α)
 
+""" Construct subobject of C-set from components of inclusion map.
+
+Recall that a *subobject* of a C-set ``X`` is a monomorphism ``α: U → X``. This
+function constructs a subobject from the components of the monomorphism, given
+as a named tuple or as keyword arguments.
+"""
+function subobject(X::T, components) where T <: AbstractACSet
+  U = T()
+  copy_parts!(U, X, components)
+  ACSetTransformation(components, U, X)
+end
+subobject(X::AbstractACSet; components...) = subobject(X, (; components...))
+
 # Finding C-set transformations
 ###############################
 

src/categorical_algebra/DPO.jl

@@ -34,18 +34,17 @@ function pushout_complement(
     orphans = Set([ m[c](x) for x in parts(L,c) if x ∉ l_image ])
     filter(x -> x ∉ orphans, parts(G,c))
   end)
-  K = typeof(G)()
-  copy_parts!(K, G, g_components)
+  g = subobject(G, g_components)
+  K = dom(g)
 
   # Construct morphism k: I → K using partial inverse of g.
   lm = compose(l, m)
   k_components = NamedTuple{ob(CD)}(map(ob(CD)) do c
     g_inv = Dict{Int,Int}(zip(g_components[c], parts(K,c)))
     [ g_inv[lm[c](x)] for x in parts(I,c) ]
   end)
-
   k = ACSetTransformation(k_components, I, K)
-  g = ACSetTransformation(g_components, K, G)
+
   return k => g
 end
 

test/categorical_algebra/CSets.jl

@@ -72,6 +72,12 @@ g, h = path_graph(Graph, 4), cycle_graph(Graph, 2)
 @test force(compose(id(g), α)) == α
 @test force(compose(α, id(h))) == α
 
+# Subobjects.
+α = subobject(g, V=[2,3,4], E=[2,3])
+@test is_natural(α)
+@test dom(α) == path_graph(Graph, 3)
+@test codom(α) == g
+
 # Limits
 #-------