Naturality: Chain Complexes and Homology Groups

This lecture covers the concept of naturality in the context of chain complexes and homology groups, focusing on the induced long exact sequence of homology groups. It discusses the naturality of the connecting homomorphisms between chain complexes, the induced diagrams of chain maps, and the commutativity of squares by functoriality. The lecture also explores the Five-Lemma in abelian groups and its application in exact sequences, emphasizing the importance of naturality in algebraic topology.