Derived functors: Identity and Homotopy Categories

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

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

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

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

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

Covers simplicial and cosimplicial objects in category theory with practical examples.

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

Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.

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

Explores natural transformations in algebra, defining functors and isomorphisms.