Lifting properties, Chapter 2(a): Definition and elementary properties of model categories

This lecture introduces the notion of morphisms having the left or right lifting property with respect to a fixed set of morphisms in a category. It also covers the closure property of morphisms with the left or right lifting property. The lecture discusses the concepts of pushouts and pullbacks, proving that sets of morphisms with lifting properties are closed under these operations. It further explores the uniqueness in the universal property of pushouts and provides examples to illustrate these concepts. The lecture concludes with an overview of lifting properties and hints at the upcoming discussion on the definition of model categories.