Topos

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Topos" – news · newspapers · books · scholar · JSTOR (July 2015) (Learn how and when to remove this message)

In mathematics, a 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; they are a direct generalization of point-set topology.^[1] The Grothendieck topoi find applications in algebraic geometry, and more general elementary topoi are used in logic.

The mathematical field that studies topoi is called topos theory.