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  "body": "\n## Summary\n\nIn a category with zero morphisms, the cokernel of a morphism $f$ is the universal morphism $q$ with $q \\circ f = 0$.\nIt is the [[coequalizer|DVSTWGVCSZ]] of $f$ and the zero morphism, and the notion dual to the [[kernel|S417YNEJ6M]].\nFor modules, the cokernel of $f \\colon X \\to Y$ is the quotient map $Y \\to Y / f(X)$.\nThe cokernel measures how far a morphism is from being surjective.\n\n## Explanations\n\n### L1 human\n\nThe image of a linear map is the part of the target that the map reaches.\nThe cokernel is what is left when one divides the target by the image: it records the directions the map misses.\nA map onto its target has zero cokernel.\nFor multiplication by $n$ on $\\Z$, the image is $n\\Z$ and the cokernel is $\\Z / n\\Z$.\n",
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