Direct Sums: Lemme 1.2

This lecture explores direct sums in the context of abelian groups. It discusses the coproduct of two abelian groups A and B, showing that A⊕B, where the injections i₁(a) = (a,0) and i₂(b) = (0,b), is a coproduct in the category of abelian groups. The lecture also covers the universal property verification and provides a detailed proof of the lemma. Various examples and properties of direct sums are presented, emphasizing the importance of understanding coproducts in the study of group theory.