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  "body": "\n## Summary\n\nAn (elementary) topos is a [[category|A2DE66937D]] with finite limits, [[exponential objects|RHWD8DY41R]] and a [[subobject classifier|NKP5TPQ79X]].\nThe category of sets is a topos, and so is the category of [[sheaves|RT8A8FJ566]] on any [[site|NYE0Z94MME]].\nA topos behaves like a universe of sets in which one can do much of mathematics, but its internal logic is in general [[intuitionistic|Q11N8X99FK]].\nToposes connect geometry, where they arise as generalized spaces, with logic, where they serve as models of higher-order theories.\n\n## Explanations\n\n### L1 human\n\nThe category of sets has products, function sets and a set $\\set{0, 1}$ of truth values that classifies subsets.\nA topos is any category with these three features.\nSets on which a fixed group acts form a topos, as do sets that vary continuously over a space (sheaves).\nIn such a world most constructions with sets still work.\nBut the law of excluded middle may fail, because a statement can be true on part of a space and false elsewhere.\n",
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