The Whitehead Lemma: Homotopy Equivalence in Model Categories

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

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

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

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

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

Explores the left homotopy relation as an equivalence relation in model categories.

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

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