Definition, synonyms and related words
Given a category ๐ with an object A, let H be a hom functor represented by A, and let F be any functor (not necessarily representable) from ๐ to Sets, then there is a natural isomorphism between Nat(H,F), the set of natural transformations from H to F, and the set F(A). (Any natural transformation ๐ผ from H to F is determined by what ๐ผ_A( mbox id_A) is.)