Notes on Cambridge Maths

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Counit

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

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