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topos
In mathematics, a topos (, or ; plural topoi or , 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 in a sense a generalization of point-set topology. The Grothendieck topoi find applications in algebraic geometry; the more general elementary topoi are used in logic.
==Grothendieck topoi (topoi in geometry)==
Since the introduction of sheaves into mathematics in the 1940s a major theme has been to study a space by studying sheaves on a space. This idea was expounded by Alexander Grothendieck by introducing the notion of a "topos". The main utility of this notion is in the abundance of situations in mathematics where topological heuristics are very effective but an honest topological space is lacking; it is sometimes possible to find a topos formalizing the heuristic. An important example of this programmatic idea to date is the étale topos of a scheme.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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