Construction of the homotopy category

Related lectures (32)

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Explores natural transformations in algebra, defining functors and isomorphisms.

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

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

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

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

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

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

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

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

Covers cylinders, path objects, and homotopy in model categories.