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In mathematics, a skeleton of a category is a subcategory which, roughly speaking, does not contain any extraneous isomorphisms. In a certain sense, the skeleton of a category is the "smallest" equivalent category which captures all "categorical properties". In fact, two categories are equivalent if and only if they have isomorphic skeletons. A category is called skeletal if isomorphic objects are necessarily identical. == Definition == A skeleton of a category ''C'' is a full, isomorphism-dense subcategory ''D'' in which no two distinct objects are isomorphic. In detail, a skeleton of ''C'' is a category ''D'' such that: *Every object of ''D'' is an object of ''C''. *(Fullness) For every pair of objects ''d''1 and ''d''2 of ''D'', the morphisms in ''D'' are precisely the morphisms in ''C'', i.e. : *For every object ''d'' of ''D'', the ''D''-identity on ''d'' is the ''C''-identity on ''d''. *The composition law in ''D'' is the restriction of the composition law in ''C'' to the morphisms in ''D''. *(Isomorphism-dense) Every ''C''-object is isomorphic to some ''D''-object. *No two distinct ''D''-objects are isomorphic. 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「Skeleton (category theory)」の詳細全文を読む スポンサード リンク
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