Derived Functors in Homotopical Algebra

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

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

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

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

Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.

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

Explores natural transformations in algebra, defining functors and isomorphisms.

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

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

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