Equivalences of Categories

Related lectures (32)

Covers the definition and properties of natural transformations between functors in category theory.

Explores the verification of a Lie functor as a left adjoint, with natural transformations satisfying triangular identities and isomorphisms.

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

Explores group actions, defining functors on groups, and verifying properties of group actions.

Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.

Explores natural transformations between functors in different categories and their applications.

Explores the construction of G-sets and left adjoint functors in category theory.

Explores functors between categories and the conditions for left and right adjoints.

Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.

Explores the concept of free abelian groups as an important left adjoint functor.

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

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

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