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This lecture discusses the concept of points fixes in G-sets, exploring the relationship between fixed points and G-sets. It covers the construction of applications between sets, the inverse application, and the equivalence between different expressions. The lecture also delves into the corestriction of applications and the construction of orbits in G-sets. The instructor demonstrates the construction of orbits and fixed points in G-sets, highlighting the adjoint relationship between different functions. The study concludes with a discussion on the generalization of these concepts to arbitrary categories.