Direct Sums: Lemme 1.2

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Page 3 of 4

Explores direct sums in abelian groups, emphasizing existence and uniqueness.

Explores the direct sum of abelian groups, emphasizing bijections and uniqueness.

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

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

Explores the construction and properties of the free abelian group FAb(X) and its categorical extensions.

Covers the proof of the Classification Theorem for finite abelian groups, demonstrating the existence of a decomposition into cyclic groups.

Covers the verification of constructions in the context of abelian groups and Sylow subgroups.

Introduces coproducts in category theory, exploring their properties, universality, and relationships with products.

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

Explores the direct sum of subgroups in an abelian group and introduces the coproduct concept in Abelian categories.