Concept

Model category

Related lectures (32)

Covers the transfer of model structures through adjunctions in the context of model categories.

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

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

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

Explores the Serre model structure on Top, focusing on right and left homotopy.

Explores lifting properties and model categories in topological spaces.

Explores the model structure on chain complexes over a field.

Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.

Explores the Serre model structure, focusing on left and right homotopy equivalences.

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

Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.

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

Explores derived functors in model categories, focusing on identity and homotopy categories.

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

Explores the existence of left derived functors in homotopical algebra, focusing on isomorphism conditions and natural transformations.

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

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

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

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

Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.