The Whitehead Lemma: Homotopy Equivalence in Model Categories

Related lectures (32)

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

Explores sets of left homotopy equivalence classes of morphisms in model categories.

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

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

Focuses on proving the construction of the homotopy category and its properties, including preservation of composition and uniqueness of functors.

Explores the basic properties of left homotopy in model categories, focusing on weak equivalences and morphism relationships.

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

Introduces left homotopy between morphisms and its preservation under postcomposition in a model category.

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

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.