Profunctor Optics: The Categorical Approach
summary
Derives profunctor optics from category theory by applying the Yoneda lemma inside the functor and profunctor categories, uses adjunctions (currying) and Tambara structure to build the free Tambara monad Phi, and shows how applying Phi to a profunctor reader yields the usual lens/prism representations. Works through coends/existentials to turn the polymorphic profunctor type for all P (P A B -> P S T) into concrete pairs of functions splitting S as C × A (lens) or C + A (prism), then recovers getter/setter-style implementations in Haskell.
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