Introduction to Category Theory: Categories and Examples

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Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

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

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

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

Introduces functors in category theory and explains their composition.

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

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

Covers the concept of natural transformations between functors and their associativity.

Explores free abelian groups, homomorphisms, and exact sequences in the context of different categories.

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.