Categorical Perspective: Abelian Groups

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Group Direct Sums in Group Theory

Explores direct sums in group theory, focusing on abelian groups and their implications.

Hom Functor: Abelian Groups

Explores the Hom functor for abelian groups and its relation to direct sums.

Direct Sums: Abelian Groups

Explores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.

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Existence of Direct Sums: Abelian Groups

Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.

Free Abelian Groups: Group Theory

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

Direct Sums: Lemme 1.2

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Abelian Groups: Free Abelian Groups

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.