Homotopical connectivity

Related lectures (32)

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

Explores natural transformations in algebra, defining functors and isomorphisms.

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

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

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

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

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

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Covers relative homotopy groups, establishing long exact sequences and defining boundary homomorphisms.