Category theory MOC Functor category Given two categories π’ and π£, we construct a functor category π£π’ where each object is a functor and each morphism is a natural transformation π :πΉ βπΊ :π’ βπ£. Special cases Endofunctor category π’π’, which possesses additional monoidal structure. Category of presheaves {π’π¨π©} tidy | en | SemBr