Homotopy Theory of Chain Complexes

Related lectures (32)

Page 3 of 4

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

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

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

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

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

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

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

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

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