Basic properties of left homotopy: The homotopy relation in a model category

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

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

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

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

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

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

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

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

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

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