categorical product

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• noun category theory Given two objects X1 and X2, their product is an object X1 × X2, with projections π1 : X1 × X2 → X1 and π2 : X1 × X2 → X2, which satisfies the following universal property: for any object Y with morphisms f1 : Y → X1 and f2 : Y → X2, there can naturally be constructed a unique morphism f : Y → X1 × X2 such that and .
• noun category theory The product generalizes, through associativity, to between more than two objects.