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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a topos is a <a href="/facts/Category_(mathematics)/7WzxUThf">category</a> that behaves like the category of <a href="/facts/Sheaf_(mathematics)/MM3hcRw4">sheaves</a> of <a href="/facts/Set_(mathematics)/BfucfHMq">sets</a> on a <a href="/facts/Topological_space/v2ut7CbK">topological space</a> (or more generally, on a <a href="/facts/Site_(mathematics)/Przxx5sH">site</a>). Topoi behave much like the <a href="/facts/Category_of_sets/LF5ykYl0">category of sets</a> and possess a notion of localization. The Grothendieck topoi find applications in <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a>, and more general elementary topoi are used in <a href="/facts/Mathematical_logic/SaI7Y3wN">logic</a>. </p><p>The mathematical field that studies topoi is called topos theory. </p>