Lectures related to Direct Sums: Abelian Groups

Categorical Perspective: Abelian Groups

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

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.

Free Abelian Groups: Group Theory

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

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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.

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.

Relation between Direct Sum and Hom

Explores the isomorphism between Hom(A, B) and Hom(A, B) for any abelian group B.

Functor Hom: Abelian Groups

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Abelian Groups: Free Abelian Groups

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

Group Theory: Verification

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

Direct Sums Arithmetic

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

Algebra: Group Actions and Direct Products

Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.

Representation Theory: Algebras and Homomorphisms

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

Direct Products in Group Theory

Explores direct products in group theory, including semi-direct products and group properties.

Direct Sums of Abelian Groups

Covers direct sums of abelian groups, group actions, and vector spaces, including coproducts and homomorphisms.

Finite Cas X and Notations

Introduces Lemma 1.14 for finite sets in Ab and discusses notations and properties of direct sums.

Endomorphisms and automorphisms of totally disconnected locally compact groups V

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing surjective homomorphisms and free abelian groups.