Group Actions: G-objects in a Concrete Category

This lecture explores the concept of G-objects in a concrete category, focusing on the categorical framework for group actions. By leveraging the adjunction in a concrete category, the notion of G acting on an object is dissected. The lecture delves into the functor U mapping objects in the category to sets, illustrating the relationship between G-objects and automorphisms. Through various examples and applications, the lecture demonstrates how G acts on objects in a concrete category, providing insights into the bijection within sets. Additionally, the lecture discusses the application of the functor U to families of objects, showcasing the relationship between G and automorphisms in the context of group actions.