Homotopy Category of a Model Category

Related lectures (32)

Page 1 of 4

Covers cylinders, path objects, and homotopy in model categories.

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

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.

Explores the Serre model structure on Top, focusing on right and left homotopy.

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.