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  "body": "\n## Summary\n\nAn additive functor is a [[functor|28NQ0KRHD3]] between [[preadditive categories|SC6FD5F4J0]] that respects the addition of morphisms.\nBetween additive categories, these are exactly the functors that preserve finite biproducts.\nHom functors, tensor products with a fixed module and derived functors are additive.\nAdditivity is the basic compatibility needed to apply a functor to chain complexes and exact sequences.\n\n## Explanations\n\n### L1 human\n\nIn a preadditive category one can add arrows between the same objects.\nAn additive functor sends a sum of arrows to the sum of their images, just as a linear map sends a sum of vectors to the sum of their images.\nFor example, tensoring with a fixed abelian group $M$ sends a homomorphism $f$ to $f \\otimes \\id_M$, and $(f + g) \\otimes \\id_M = f \\otimes \\id_M + g \\otimes \\id_M$.\nAdditive functors take direct sums to direct sums, so they can be computed piece by piece.\n",
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