Lectures related to Mapping cylinder

Explores the comparison of long exact sequences for vibrations and the relationship between homotopy and homology groups.

Discusses how CW pairs satisfy the homotopy extension property through retractions and homotopy extension properties.

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

Covers the definition and properties of a model category, including fibrations, cofibrations, weak equivalences, and more.

Explores the cylinder construction on a chain complex and its equivalence to chain homotopy.

Explores the homotopy lifting property, demonstrating how to lift homotopic maps and solve lifting problems on different spaces.