Lectures related to Group Actions: G-objects in a Concrete Category

Explores actions on products in group theory, including automorphism construction and preservation of products.

Explores building categories from graphs and the encoding of information by functors.

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Explores natural transformations in algebra, defining functors and isomorphisms.

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

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

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

Explores the construction of the free action functor and its equivariance.

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

Provides an overview of categories, functors, and natural transformations in mathematics.

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

Covers group quotient, group actions, and functors connecting sets and G-sets.

Explores constructing desired adjoints in specific categories like Set.

Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.

Covers simplicial and cosimplicial objects in category theory with practical examples.