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  "body": "\n## Summary\n\nIn a category with zero morphisms, the kernel of a morphism $f$ is the universal morphism $k$ with $f \\circ k = 0$.\nIt is the [[equalizer|CTJ5AD8ST5]] of $f$ and the zero morphism.\nIn categories of groups, modules or vector spaces it is the inclusion of the usual [[kernel|0W88CEGQP1]], the set of elements sent to zero.\nKernels and their dual notion, cokernels, are the building blocks of abelian categories.\n\n## Explanations\n\n### L1 human\n\nThe kernel of a linear map is the set of vectors that it sends to zero.\nCategory theory cannot look at elements, so it describes this subspace by a property of its inclusion map.\nThe inclusion is killed by $f$, and every other map that is killed by $f$ passes through it in exactly one way.\nFor the map $\\Z \\to \\Z/2$ that reduces mod $2$, the kernel is the inclusion of the even integers $2\\Z \\to \\Z$.\n",
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