Lecture
This lecture explores examples of category equivalences and non-equivalences, starting the study of an adjunction example related to group actions. It delves into the concept of equivalence between categories, consisting of a pair of functors F, G: D → C, with natural isomorphisms. The lecture also discusses the implications of categories being equivalent, the natural transformations involved, and specific examples of adjunctions. Furthermore, it covers the composition of functors, the action of groups on objects, and the conditions for an adjunction between two categories. The lecture concludes by examining the associativity of composition in category theory and the requirements for a functor to be G-equivariant.