A bifunctor is a functor whose domain is a product category. Thus a covariant bifunctor
from 
and 
to 
is a functor
 |
It assigns an object 
to each pair of objects and a morphism 
to each pair of morphisms,
preserving identities and composition. A bifunctor
can instead be contravariant in either argument, as in the Hom
functor 
,
where 
denotes the category
of sets.
