Homotopy Category and Derived Functors

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

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

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

Explores the model structure on chain complexes over a field.

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

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Explores the Serre model structure on Top, focusing on right and left homotopy.

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

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

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