Lecture
This lecture covers the direct sum of subgroups in an abelian group, where the sum of two subgroups is defined as the set of all formal sums of elements from each subgroup. The direct sum is denoted as B⊕C, and if the intersection of the subgroups is {0}, it is called a direct sum. The lecture also introduces the coproduct of subgroups in Abelian categories, illustrating the concept with mathematical notations and diagrams.