Foundations of mathematics | Sheaf theory | Topos theory

Topos

In mathematics, a topos (UK: /ˈtɒpɒs/, US: /ˈtoʊpoʊs, ˈtoʊpɒs/; plural topoi /ˈtoʊpɔɪ/ or /ˈtɒpɔɪ/, 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. The Grothendieck topoi find applications in algebraic geometry; the more general elementary topoi are used in logic. The mathematical field that studies topoi is called topos theory. (Wikipedia).

Topos
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