Lectures related to Exact Sequences in Abelian Groups

Functor Hom: Abelian Groups

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

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Exact Sequences in Abelian Groups

Explains split exact sequences in abelian groups, emphasizing the role of sections and retractions.

Group Cohomology

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

Group Operations and Homomorphisms in Abelian Groups

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

Group Direct Sums in Group Theory

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

The Lemma of the Five: Abelian Groups

Presents the Lemma of the Five, a fundamental result in group theory.

Categorical Perspective: Abelian Groups

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

Relation between Direct Sum and Hom

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

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.