Examples of Quasicategories

This lecture explores two examples of quasicategories, focusing on Kan complexes and Nerves of categories. The instructor explains how every Kan complex is a quasicategory, leading to the concept of a homotopy category. The lecture delves into the relationship between Kan complexes and quasicategories, highlighting the inclusion factor from Kan complexes to quasicategories and discussing the left adjoint. The discussion also covers the homotopy category of a Kan complex, emphasizing the objects and morphisms within it. The lecture concludes with a broader theorem involving an adjunction between quasicategories and categories, showcasing the right adjoint as the nerve and the left adjoint as the homotopy category.