Lectures related to Homotopy Type Theory

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

Covers the concept of degree in homotopy theory and the structure of complexes with two simplices.

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

Explores the extension property of spaces and the recognition principle for cofibrations.

Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.

Covers the concept of homotopy classes and their properties in topology, including short components and group concatenation.

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

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

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