Figure 1. Direct product: If S, M1, M2 are objects of the category C , then S is the direct product if we can find an object X and morphisms k1 : S ! M1, k2S ! M1, f : X ! M2, and c : X ! M2 such that there is a unique morphism u : X ! S. The direct product is a generalization of the familiar concept of the Cartesian product of two sets to arbitrary categories.
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