A coproduct is a colimit of a discrete diagram: it has injections from each summand and every family of maps out of the summands extends uniquely across it.
A countable coproduct is indexed by the natural numbers. In the Category of sets it is the disjoint union .
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In category theory, a coproduct is a generalization of the concept of a disjoint union of sets, and more broadly, it can be thought of as a way to combine objects in a category. The coproduct of a collection of objects provides a means of "merging" these objects while preserving their individual identities.