Introduction to Left Homotopy: The Homotopy Relation in a Model Category

Related lectures (32)

Page 1 of 4

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

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

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

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

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

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

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