Homotopy category of chain complexes

Related lectures (32)

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.

Explores acyclic fibrations and cylinder objects in chain complexes.

Covers the long exact sequence of relative homology groups and chain complexes.

Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.

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

Explains relative homology, n-cycles, n-boundaries, and exact sequences of chain complexes.

Focuses on proving the construction of the homotopy category and its properties, including preservation of composition and uniqueness of functors.

Explores the characterization of fibrations and acyclic fibrations in chain complexes.

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

Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.

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