Quillen pairs and Quillen equivalences: Derived functors

Related lectures (32)

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

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

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

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

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

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

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

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.

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

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