Lecture
This lecture introduces the concept of quasicategories as an alternative approach to defining homotopy maps and categories, in comparison to model categories. The instructor reviews the course's progression from basic category theory to model structures, and now to quasicategories, explaining how quasicategories can also lead to homotopic maps and categories. The lecture is divided into four parts, covering the definition of quasicategories, their relation to model categories and simply enriched categories, the model structure of quasicategories, and the benefits of using quasicategories over model categories.