Homotopy Theory of Chain Complexes

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

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

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

Explores the homotopy theory of chain complexes, focusing on defining cylinder objects and left homotopy.

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

Explores acyclic fibrations and cylinder objects in chain complexes.

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

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

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

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