Theory: Adjunctions

This lecture introduces the notion of adjunction between categories, emphasizing the generalization of the equivalence of categories. The instructor establishes the key idea and provides a detailed definition of adjunctions through natural transformations. The lecture further explores the characterization of adjunctions, highlighting the necessary conditions for a pair of functors to form an adjunction. Various diagrams and propositions are presented to illustrate the concept, culminating in a discussion on the natural isomorphism between the functors involved. The lecture concludes with a pause for reflection on the defined functors.