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  "body": "\n## Summary\n\nA subobject classifier in a [[category|A2DE66937D]] with finite limits is an object $\\Omega$ with a morphism $\\top \\colon 1 \\to \\Omega$.\nEvery [[subobject|FS1FKAE89H]] of every object $X$ must be the pullback of $\\top$ along exactly one morphism $X \\to \\Omega$.\nIn the category of sets, $\\Omega = \\set{0, 1}$ and the morphism $X \\to \\Omega$ of a subset is its [[characteristic function|0V5B6D6BQH]].\nIt is one of the defining features of a [[topos|6837RS7N82]], and $\\Omega$ plays the role of the object of truth values.\nIn a sheaf topos, $\\Omega$ need not have two elements, and its internal logic is in general [[intuitionistic|Q11N8X99FK]].\n\n## Explanations\n\n### L1 human\n\nIn sets, a subset $A \\subseteq X$ is the same as a yes/no question on $X$: \"is $x$ in $A$?\".\nA subobject classifier is an object $\\Omega$ of answers that makes this work in another category.\nFor example, in sheaves on a space $X$, the answers over an open set $U$ are the open subsets of $U$.\nThe truth value of \"$s = t$\" for two sections is the open set where they agree.\nSo truth values come in many shades, not just true and false.\n",
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