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  "body": "\n## Summary\n\nA biproduct of two objects is a single object that is at the same time their [[product|S5744QZV4N]] and their [[coproduct|4FJ0S71P58]], with compatible projections and inclusions.\nIt generalizes the direct sum $A \\oplus B$ of abelian groups or modules, which has both universal properties.\nAdditive categories are the preadditive categories with a zero object in which all binary biproducts exist.\nIn a preadditive category, a finite product is automatically a biproduct.\n\n## Explanations\n\n### L1 human\n\nThe direct sum $\\R^2 = \\R \\oplus \\R$ can be seen in two ways.\nIt is built from two copies of $\\R$ by taking pairs, with the two coordinate projections.\nIt also receives the two copies of $\\R$ as the axes, so that a pair of maps out of the two copies combines into one map out of $\\R^2$.\nA biproduct is an object with both these features, where projecting after including the same copy gives the identity and after including the other copy gives zero.\n",
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