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In mathematics, a canonical map, also called a natural map, is a map or morphism between objects that arises naturally from the definition or the construction of the objects. A closely related notion is a structure map or structure morphism; the map that comes with the given structure on the object. They are also sometimes called canonical maps. Examples: *If ''N'' is a normal subgroup of a group ''G'', then there is a canonical map from ''G'' to the quotient group ''G/N'' that sends an element ''g'' to the coset that ''g'' belongs to. *If ''V'' is a vector space, then there is a canonical map from ''V'' to the second dual space of ''V'' that sends a vector ''v'' to the linear functional ''f''''v'' defined by ''f''''v''(λ) = λ(''v''). *If ''f'' is a ring homomorphism from a commutative ring ''R'' to commutative ring ''S'', then ''S'' can be viewed as an algebra over ''R''. The ring homomorphism ''f'' is then called the structure map (for the algebra structure). The corresponding map on the prime spectra: Spec(''S'') →Spec(''R'') is also called the structure map. *If ''E'' is a vector bundle over a topological space ''X'', then the projection map from ''E'' to ''X'' is the structure map. 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「canonical map」の詳細全文を読む スポンサード リンク
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