Post #3023667
2026-05-13 19:26 UTC
@BartoszMilewski@mathstodon.xyz @6d03@mathstodon.xyz Thanks, I don't have a direct answer to this, but it did gave me an idea. It is possible to encode the graph of a thin profunctor, which has at most one element for a given source and target object. There's still no guarantee that the morphisms are commuting squares, but that's common in Haskell-style category theory. (Requiring the source and target categories to be thin too would fix that.) https://github.com/sjoerdvisscher/proarrow/blob/main/src/Proarrow/Category/Instance/Graph.hs
Replies (2)
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@BartoszMilewski@mathstodon.xyz 2026-05-13 21:15
@sjoerd_visscher@types.pl @6d03@mathstodon.xyz This is also known as a Bool-enriched profunctor
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@sjoerd_visscher@types.pl 2026-05-14 08:45
@BartoszMilewski@mathstodon.xyz I was confused here, the morphisms are always correct too, because the “diagonals” are elements of the profunctor which must be equal in case of a thin profunctor.