definition. n-fold (co)products [kostecki2011introduction, 2.22] [tt-0011]

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In any category with binary products the objects \(X \times (Y \times Z)\) and \((X \times Y) \times Z\) are isomorphic. In any category with binary coproducts the objects \(X+(Y+Z)\) and \((X+Y)+Z\) are isomorphic.

This allows to consider \(n\)-fold products \(X_1 \times \dots \times X_n\) and \(n\)-fold coproducts \(X_1 + \dots + X_n\) of objects of a given category.