Homotopy Theory in Care Complexes

Related lectures (32)

Page 1 of 4

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

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

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 retractions and model category structures.

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

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Focuses on lifting properties in homotopy theory of chain complexes.

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

Explores the model structure on chain complexes over a field.