Group Operations and Homomorphisms in Abelian Groups

Related lectures (32)

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

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

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

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

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

Introduces functors in category theory and explains their composition.

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.

Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

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

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