Model Categories: Properties and Structures

This lecture covers the properties and structures of model categories, focusing on the themes of properties of model categories, left homotopy, and universal properties of limits. It delves into the construction of factorizations, the Strøm model structure on Top, and the explicit model structures from model structure on Top. The lecture also explores the algebraic model category, the lifting axioms, and the construction of the factorization. Additionally, it discusses the concept of homotopy of continuous maps, the cylinder on chain complexes, and the lifting axioms in the context of chain complexes.