Lectures related to Notation: Coproduct vs. Product

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

Covers the existence and uniqueness of direct sums in abelian groups.

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

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

Covers exact sequences, torsion, divisibility, and operations on abelian groups.

Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.

Explores group operations with cyclic properties and the universal ownership of quotients.

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

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

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.