Natural Transformations: Categories, Functors, and Equivalence

This lecture introduces the concept of natural transformations between functors, defined as maps between objects and morphisms in categories. The instructor explains the commutativity of diagrams and the associativity of compositions. Examples illustrate the identity natural transformation and the equivalence of categories. The lecture also covers the universal properties of discrete and trivial topologies, emphasizing the existence of natural transformations in various contexts.