Homotopical Algebra: (Co)Limits

This lecture covers the concept of (co)limits in homotopical algebra, exploring the relationship between functors in small categories and the colimits and limits. The instructor discusses the simplex category, functor relations, and special cases. The lecture delves into the universal properties of colimits and limits, providing insights into the structure maps and terminal objects. Additionally, the lecture presents natural isomorphisms and the intuition behind (co)limits. The session concludes with a detailed explanation of pushouts and their significance in homotopical algebra.