Homotopical Algebra

Related lectures (32)

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

Explores the concept of category equivalence through isomorphic functors and natural isomorphisms between categories.

Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.

Explores homotopical algebra, covering colimits, limits, adjunctions, and their applications in group theory.

Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.

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

Delves into homotopical algebra, defining functors and adjunctions with examples.

Introduces adjunctions in Group Theory with examples of natural transformations and isomorphisms.

Explores the concept of category theory, providing examples and discussing the opposite category concept.

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