1. Functors are introduced as structure-preserving maps between categories, followed by natural transformations, which are families of morphisms relating functors.
2. Vertical and horizontal compositions of natural transformations, lead to the notion of functor categories.
   1. Natural isomorphisms and essentially surjective functors help define equivalence between categories.
   2. Notable examples of equivalences: monoids and one-object categories, finite-dimensional vector spaces and matrix categories.

Functors

Natural transformations