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  "body": "\n## Summary\n\nAn additive category is a [[preadditive category|SC6FD5F4J0]] with a zero object in which any two objects have a [[biproduct|BZEJKTQ76T]].\nIts morphisms between finite direct sums can be written as matrices of morphisms, composed by matrix multiplication.\nCategories of modules, of free modules and of vector bundles are additive.\nAdditive categories are the natural home of chain complexes and of the homotopy category of chain complexes.\n\n## Explanations\n\n### L1 human\n\nIn an additive category one can add maps, and one can form direct sums of objects.\nA map from $A \\oplus B$ to $C \\oplus D$ is then a $2 \\times 2$ matrix whose entries are maps from $A$ or $B$ to $C$ or $D$.\nThis is exactly how one computes with linear maps between spaces split into pieces.\nFor example, finite-dimensional vector spaces over a field form an additive category, and a linear map $K^2 \\to K^3$ is a $3 \\times 2$ matrix.\n",
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