Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.
Introduces the construction of quasi-categories from Kan enriched categories through defining simplicially enriched categories and constructing the simplicial nerve functor.
Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.
Covers the combinatorics of the simplex category and its equivalence to topological spaces, as well as the concept of functor categories for cosimplicial and simplicial objects.
Covers the construction of a left adjoint to the singular set functor, comparing the homotopy theory of topological spaces with that of simplicial sets.
Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.
