Doesn’t that construction only work in categories that also contain their own morphisms as objects since a profunctor maps
(Cᵒᵖ × C) → Setand not the same like(Cᵒᵖ × C) → C? Since the category of Haskell types special, containing its own morphisms, so the profunctor could be like(haskᵒᵖ × hask) -> hask? or I just don’t understand it.I don’t nearly know enough to understand this but is anyone willing to help me get the thing on the top :>
To first give you some context, the thing on the top is from The “Representable Functors” chapter of Category Theory for Programmers. So technically, you only need to read 230 Pages of a maths textbook to get it ;)
But this isn’t exactly what you asked for, so I’ll try to help you get it as best I can with my limited understanding of the subject. First of all it would be helpful to know what your prior knowledge in Maths, especially Set theory, is?