(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”