Homotopical Algebra: Functor and Adjunctions

Related lectures (32)

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

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

Explores concrete examples of limits and colimits in functors and different categories.

Introduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.

Delves into the computation and geometric realization of small categories, exploring the relationship between nerves and geometric structures.

Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.

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

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

Introduces functors, including identity and forgetful functors, and explores duality functors.

Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Introduces limits and colimits in a category, covering their properties and uniqueness.

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