Adjunction is the “weakening of Equality” in Category Theory.
Equivalence of 2 Categories if:
5.2 Adjunction definition: such that the 2 triangle identities below ( red and blue) exist.
6.1 Prove: Let C any category, D a Set.
1 = Singleton in Set D
From an element in the singleton Set always ‘picks’ (via the function) an image element from the other Set, hence :
Examples : Product & Exponential are Right Adjoints
Note: Adjoint is a more powerful concept to understand than the universal construction of Product and Exponential.
With Product (Left Adjoint) and Exponential (Right Adjoint) =>