Lectures related to Triangular Identities

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

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

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

Introduces natural transformations in category theory through concrete examples from group theory.

Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.

Explores a concrete example of adjunction in category theory and covers natural transformations and group theory concepts.

Explores adjunctions, triangular identities, and natural transformations in category theory.

Introduces an important generalization of category equivalence and its implications for group theory.

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

Explores the definition of orbits and fixed points of a G-object in any category, focusing on G-equivariant applications.

Covers the construction and universal properties of pushouts in group theory.

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

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

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

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

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

Explores the restriction functor in group theory, focusing on its properties.

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

Explores adjunctions and mutual inverses alpha and beta in category theory.

Introduces the theory of categories through examples and discusses the product of categories.