(Note that we write compositions from left to right and accordingly apply most maps on the right.)
Def.1
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
.
Def.2
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”