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Stream: learning: questions

Topic: Does Prof have (at least some) inserters?

fosco (Mar 27 2024 at 12:58):

More precisely: is it possible to consider "algebras" for an endo-profunctor $P : {\cal C} \rightsquigarrow {\cal C}$ as inserters of $P$ and hom?

fosco (Mar 27 2024 at 13:01):

(I suspect it does not, with some negative thinking in Prof{0,1} = Rel)

John Onstead (Mar 27 2024 at 19:22):

Not sure if this helps but there is already a notion of algebra for a profunctor. There was some discussion on this server a while back about it, and I believe if I remember correctly categories of algebras of profunctors corresponded to generic inserters in Cat between any two parallel functors out of C (not just a functor and a hom functor) since they generalized algebras for endofunctors like how profunctors generalize functors. Hope that helps!