For a category 
, the Hom functor is the bifunctor
 |
where 
denotes the category
of sets. The Hom functor sends a pair 
to the set 
of morphisms from 
to 
. In the first argument it reverses the direction of each morphism, while in the second argument it preserves that
direction. Holding 
fixed gives the covariant functor 
, while holding 
fixed gives the contravariant
functor 
.
