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  "body": "\n## Summary\n\nThe coequalizer of two parallel morphisms $f, g \\colon X \\to Y$ in a [[category|A2DE66937D]] is a universal morphism $q \\colon Y \\to Q$ with $q \\circ f = q \\circ g$.\nIt is the [[colimit|BJS1CGTKQ5]] of the diagram formed by $f$ and $g$, and it is dual to the [[equalizer|CTJ5AD8ST5]].\nIn sets it is the quotient of $Y$ that identifies $f(x)$ with $g(x)$ for each $x$.\nIn abelian groups it is the cokernel of $f - g$.\n\n## Explanations\n\n### L1 human\n\nGiven two functions $f$ and $g$ from $X$ to $Y$, glue $f(x)$ to $g(x)$ in $Y$ for every $x$, and keep gluing until the identifications are consistent.\nThe result is a quotient set $Q$ of $Y$, and $q$ sends each element of $Y$ to its glued class.\nFor example, let $X = \\{*\\}$, $Y = [0, 1]$, $f(*) = 0$ and $g(*) = 1$.\nThe coequalizer glues the two ends of the interval, and with the quotient topology it gives a circle.\n",
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