Homotopy Theory of Chain Complexes

Related lectures (32)

Page 2 of 4

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

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

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

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

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

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

Explores acyclic fibrations and cylinder objects in chain complexes.

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

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

Explores derived functors in model categories, focusing on identity and homotopy categories.