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

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 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.

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.

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

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

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

Explores sets of left homotopy equivalence classes of morphisms in model categories.

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