Lectures related to Free Action Functor: Left Adjoint to Forgetful Functor

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

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

Explores the construction of the free action functor in group theory and category theory, emphasizing group actions and their properties.

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

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

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.

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

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

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

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

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.

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.

Delves into the categorical framework for group actions and the correspondence between G-actions on c and functors from BG to C.

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

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

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

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

Explains the concept of free actions and their preservation properties in group theory.