Lectures related to Localization of a category

Explores lifting properties and model categories in topological spaces.

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.

Concludes the proof of the existence of left derived functors and discusses total left and right derived functors.

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

Covers cohomology, injective resolutions, and acyclic objects in an abelian category.

Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.

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