“Adjunction arises everywhere” — MacLane. Adjunction provides a perspective on universal properties.

1. Definition of adjoint functors
2. Naturality axiom and its equivalent formulations.
3. Examples of adjoint functors, including: a) Free and forgetful functors in algebraic structures b) Discrete and indiscrete topologies c) Diagonal functor and its adjoints
4. Relationship between adjoint functors and initial/terminal objects.
5. Unit and counit of an adjunction.

Transpose and naturality definition

Adjunctions via units and co-units