Make pointed-set categories and schemas actually pointed #857
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epatters
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Sep 29, 2023
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Thanks for the PR. With the idea that Catlab.Theories should contain a hierarchy of plausibly useful theories even if we don't immediately need them, I might suggest having:
ThPointedSetCategoryfor a category enriched in pointed sets, as beforeThPointedCategoryfor a pointed category inherits fromThPointedSetCategory, adding the zero objects.
| """ | ||
| @theory ThPointedSetCategory{Ob,Hom} <: ThCategory{Ob,Hom} begin | ||
| @theory ThPointedCategory{Ob,Hom} <: ThCategory{Ob,Hom} begin | ||
| ZeroOb()::Ob |
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Our convention for term constructors in Catlab.Theories is that they are lowercase.
| zeromap(A,B)::Hom(A,B)⊣(A::Ob,B::Ob) | ||
| compose(zeromap(A,B),f::(B→C))==zeromap(A,C)⊣(A::Ob,B::Ob,C::Ob) | ||
| compose(g::(A→B),zeromap(A,B))==zeromap(A,C)⊣(A::Ob,B::Ob,C::Ob) | ||
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| #f == g ⊣ (A::Ob,f::Hom(A,ZeroOb()),g::Hom(A,ZeroOb())) | ||
| #f == g ⊣ (B::Ob,f::Hom(ZeroOb(),B),g::Hom(ZeroOb(),B)) |
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Why have commented out axioms?
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Documentation on your documentation.
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I original left out zero objects in
PtdSetCategoryandPtdSetSchemabut now I want theAttrside to be allowed to have a zero object so that I can pull attrs out of a hat that aren't in the source schema; I'm not sure whether I really need the zero object in the combinatorial side yet but why tempt fate?