The categorical notion which is dual to product. The coproduct of a family {X_i}_(i element I) of objects of a category is an object C = coproduct_(i element I) X_i, together with a family of morphisms {c_i :X_i->C}_(i element I) such that for every object D and every family of morphisms {d_i :X_i->D} there is an unique morphism d:C->D such that d°c_i = d_i for all i element I. The coproduct is unique up to isomorphisms.
