(Note that we write compositions from left to right and accordingly apply most maps on the right.)
A functor is called a left adjoint to a functor if there is a bijection between the homsets:
natural in both and . In this case is called a right adjoint to , and we write .
A functor is called a left adjoint to a functor if there are natural transformations and satisfying the zig-zag identities:
So, why are these two definitions equivalent?
Continue reading “On the two definitions of adjunctions”