Lecture
This lecture introduces the definition of a model category, a category with extra structure enabling the definition of homotopy of morphisms. It covers the axioms of a model category, including the 2-out-of-3 axiom, retraction axiom, lifting axiom, and factorization axiom. The lecture also discusses the properties of fibrations, cofibrations, weak equivalences, acyclic fibrations, acyclic cofibrations, cofibrant and fibrant objects, and bifibrant objects.