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n (context|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 $\backslash pi\_1\; \backslash circ\; f\; =\; f\_1$ and $\backslash pi\_2\; \backslash circ\; f\; =\; f\_2$.

n (context|category theory) The product generalizes, through associativity, to between more than two objects.