Group Theory: Restriction Functor

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Introduces functors in category theory and explains their composition.

Introduces the concept of restriction functors in group actions.

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

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

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

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

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

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

Covers examples of categories like sets, groups, and vector spaces, exploring composition and product formation.

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