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  "body": "\n## Summary\n\nThe kernel pair of a morphism $f \\colon X \\to Y$ is the [[pullback|Q05K04QJ71]] of $f$ along itself.\nIt records which pairs of elements $f$ sends to the same place.\nSo it is the categorical form of the equivalence relation induced by a map.\nA morphism $f \\colon X \\to Y$ is a [[monomorphism|Y2NP1JFR86]] exactly when $X$ with two identity maps is a kernel pair of $f$.\nIn a [[regular category|2SM3JRJXA4]], a regular epimorphism is the coequalizer of its kernel pair.\n\n## Explanations\n\n### L1 human\n\nA function can send different inputs to the same output.\nThe kernel pair collects all pairs of inputs with the same output.\nFor the map from the integers to the remainders modulo $3$, it is the set of pairs $(a, b)$ with $a - b$ divisible by $3$.\nFor a group homomorphism, it carries the same information as the kernel.\n",
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