Elementary Properties of Model Categories

Related lectures (32)

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

Covers cylinders, path objects, and homotopy in model categories.

Covers the definition and properties of a model category, including fibrations, cofibrations, weak equivalences, and more.

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

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

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

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

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

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.