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Subobject classifier + Internal hom for C-Sets #786
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Thanks Kris! Wonderful to see how slickly we can now implement these features.
I left a few comments below.
Also, I would like to have a generic interface for subobject classifiers and internal homs, which we would then implement for FinSet as well as C-Set. However, that can wait for a future PR.
For future reference, we had to change the definition of @present ThInitial(FreeSchema) begin
I::Ob
end
@acset_type Initial(ThInitial)
I = generators(ThInitial)[1]
G = path_graph(Graph,3)
dG = FinDomFunctor(G)
bang = FinFunctor(
Dict(:E => :I, :V => :I),
Dict(:src => id(I), :tgt => id(I)),
SchGraph, ThInitial)
I1 =FinDomFunctor(apex(terminal(Initial)))
α = Dict(:V=>FinFunction([1,1,1]), :E=>FinFunction([1,1]))
DiagramHom{id}(bang, α, dG, I1) |
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cleanup
Diagrams comes before CSets now Accessor to get the ACSet of an ACSetFunctor Add schema equations to ACSetFunctor components kw for sigma migration to return a diagram morphism
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Combines subacset search with computation of representables.
Tested on DDS (with equations to make the repr finite), Grph, and ReflGrph.
A change to SigmaMigration was needed because the previous implementation threw away the diagram map data (how the input CSet is related to the output CSet). Maybe should return a proper DiagramHom, but for now it's just the result ACSet + a dictionary of the diagram map components.
Shoutout to @KevinArlin for helping me work out where the homs go in the subobject classifier + internal hom constructions!