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In mathematics, a classifying topos for some sort of structure is a topos ''T'' such that there is a natural equivalence between geometric morphisms from a cocomplete topos ''E'' to ''T'' and the category of models for the structure in ''E''. ==Examples== *The classifying topos for objects of a topos is the topos of presheaves over the opposite of the category of finite sets. *The classifying topos for rings of a topos is the topos of presheaves over the opposite of the category of finitely presented rings. *The classifying topos for local rings of a topos is the topos of sheaves over the opposite of the category of finitely presented rings with the Zariski topology. *The classifying topos for linear orders with distinct largest and smallest elements of a topos is the topos of simplicial sets. *If ''G'' is a discrete group, the classifying topos for ''G''-torsors over a topos is the topos ''BG'' of ''G''-sets. *The classifying space of topological groups in homotopy theory. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Classifying topos」の詳細全文を読む スポンサード リンク
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