Categorical Perspective: Abelian Groups

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Direct Sums Arithmetic

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

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.

Direct Sums of Abelian Groups

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

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.

Group Cohomology

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

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Group Theory: Direct Sum of Abelian Groups

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Group Theory: Verification

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

Algebra: Group Actions and Direct Products

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