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  "body": "\n## Summary\n\nA pushout is the [[colimit|BJS1CGTKQ5]] of a diagram made of two morphisms with a common source.\nIt glues two objects together along the images of a third object.\nPushouts give gluing of spaces, amalgamated free products of groups and tensor products of commutative rings.\nIt is the dual notion of a [[pullback|Q05K04QJ71]].\n\n## Explanations\n\n### L1 human\n\nTake two objects $X$ and $Y$ and a common piece $Z$ that maps into both.\nThe pushout is the smallest object in which $X$ and $Y$ sit side by side and the two copies of $Z$ are glued into one.\nFor sets, take the disjoint union of $X$ and $Y$ and identify $f(z)$ with $g(z)$ for each $z$ in $Z$.\nFor example, gluing two closed intervals at one end point gives a longer interval.\nIn the same way, gluing two discs along their boundary circles gives a sphere.\n",
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