Derived functors: Two technical lemmas

Related lectures (32)

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

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

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

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

Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.

Covers the Fundamental Theorem of homotopical algebra, Quillen pairs, and derived functors.

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

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

Explores the model structure on chain complexes over a field.

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