Functor

Hom-functor

The Hom-functor is a bifunctor, contravariant in its first argument and covariant in its second, for a locally small category .

On objects, it maps to the Hom-set of morphisms with domain and codomain .

The morphism map for fixed domain is the covariant pushforward

while the morphism map for fixed codomain is the contravariant pullback

Since the following diagram commutes

this indeed forms a bifunctor.

---

tidy| en | sembr