Natural Transformations: Categories, Functors, and Equivalence

Related lectures (32)

Page 3 of 4

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

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

Explores constructing desired adjoints in specific categories like Set.

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

Explores defining functors on morphisms, fixed points, orbits, equivariance, and composition preservation.

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

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Covers the concept of isomorphism in categories, defining morphisms with inverses and exploring automorphisms and groupoids.

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

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