Quasicategories and Homotopy Categories

Related lectures (32)

Page 3 of 4

Explores infinity category theory, covering ABB, Kao-cosmos, homotopy, categories, and equivalences.

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Covers the characterization of trivial Kan fibrations and the importance of homotopy coherent groups.

Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Explores three ways to form quotient spaces using group actions and equivalence relations.

Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.

Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.

Discusses the benefits of quasi-category theory and model structures.