The Simplex Category: Simplicial Sets

This lecture introduces the combinatorics of the simplex category, a category that allows defining homotopy theory equivalent to that of topological spaces. It covers the definition of the simplex category, the concept of coface and codegeneracy maps, and the cosimplicial identities. The lecture also explores the functor categories Fun(A,C) and Fun(AOP, C) as categories of cosimplicial and simplicial objects in C, respectively.