Direct Sum

A construction that forms a new object from a family of objects by taking tuples and allowing only finitely many nonzero components (in the usual algebraic finite direct-sum case), with componentwise operations and injections from each summand.

A construction that combines a family of modules or groups into a larger object consisting of tuples with finitely many nonzero components, with operations defined componentwise; it serves as the coproduct in the category of modules.