Sets of Left Homotopy Classes: The Homotopy Relation in a Model Category

Related lectures (32)

Page 3 of 4

Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.

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

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

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

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

Explores the equivalence of left and right homotopy for morphisms between bifibrant objects.

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

Explores the homotopy theory of chain complexes over a field, focusing on closure properties and decomposition.

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

Explores the model structure on chain complexes over a field.