Hom Functor: Abelian Groups

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Related lectures (31)

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Free Abelian Group: Construction and Properties

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

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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.

Group Operations and Homomorphisms in Abelian Groups

Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.

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.

Direct Sums: Lemme 1.2

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

Direct Sums Arithmetic

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Representation Theory: Algebras and Homomorphisms

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

Group Theory: Special Cases

Covers special cases in group theory, focusing on group actions and functors.

Group Theory: Verification

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