Topos

In mathematics, a Grothendieck topos (US: /ˈtɒpɒs/, UK: /ˈtoʊpoʊs, ˈtoʊpɒs/; plural topoi /ˈtɒpɔɪ/ or /ˈtoʊpɔɪ/, or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally, on a site). Topoi behave much like the category of sets and possess a notion of localization. Grothendieck topoi find applications in algebraic geometry. They are generalized by elementary topoi, which are used in logic.

The mathematical field that studies topoi is called topos theory.

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