Let and . Given an Adjunction there is a Natural Transformation such that in corresponds to in

This is a dual notion to a Unit.

Triangular Identities

Lemma

Let be an Adjunction with counit . Then is pointwise Epimorphism if and only if is Faithfull.

Proof

Lemma

Let be an Adjunction with counit . Then is Isomorphic if and only if is Full and Faithfull.

Proof