An adjoint functor is one member of a pair of functors 
and 
for which there is a bijection
 |
that is natural in the objects 
and 
. In this situation, 
is left adjoint to 
, and 
is right adjoint to 
. The natural bijection is equivalently
described by a unit and counit satisfying the triangle identities. Left adjoints
preserve colimits, while right adjoints preserve limits.
