Homotopy Theory of Chain Complexes

Related lectures (32)

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Explores the model structure on chain complexes over a field.

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

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

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

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

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

Explores the Serre model structure on Top, focusing on right and left homotopy.

Focuses on lifting properties in homotopy theory of chain complexes.

Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.