Quasicategories and Homotopy Categories

Related lectures (32)

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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.

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

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

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

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

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

Covers natural transformations between functors, identity transformations, and equivalence of categories.

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.