Free Abelian Group: Construction and Properties

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Related lectures (32)

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Free Abelian Groups: Group Theory

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

Hom Functor: Abelian Groups

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

Relation between Direct Sum and Hom

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

Divisibility and Torsion

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

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Functor Hom: Abelian Groups

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

Direct Sums in Abelian Groups

Explores direct sums in abelian groups, emphasizing existence and uniqueness.

Invariant Definitions

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

Group Operations and Homomorphisms in Abelian Groups

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

Adjunctions and Limits: Exploring Functors and Co-limits

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.