Free Action Functor: Left Adjoint to Forgetful Functor

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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.