Generalization of Category Equivalence

This lecture introduces an important generalization of the concept of category equivalence, focusing on the machinery of natural transformations. The notion of adjunction is defined in terms of a pair of functors in different domains, equipped with natural transformations. The instructor spends a significant portion of the lecture dissecting this definition, which will be crucial when applying category theory to group theory. The goal is to explore examples and implications of this generalization, particularly in the context of group theory.