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In category theory, a branch of mathematics, a rigid category is a monoidal category where every object is rigid, that is, has a dual ''X'' * (the internal Hom ''(1 )'') and a morphism 1 → ''X'' ⊗ ''X'' * satisfying natural conditions. The category is called right rigid or left rigid according to whether it has right duals or left duals. They were first defined (following Alexandre Grothendieck) by Neantro Saavedra-Rivano in his thesis on Tannakian categories.〔 * N. Saavedra Rivano, ''Catégories Tannakiennes'', Springer LNM 265, 1972〕 == Definition == There are at least two equivalent definitions of a rigidity. *An object ''X'' of a monoidal category is called left rigid if there is an object ''Y'' and morphisms and such that both compositions are identities. A right rigid object is defined similarly. An inverse is an object ''X−1'' such that both ''X'' ⊗ ''X−1'' and ''X−1'' ⊗ ''X'' are isomorphic to 1, the one object of the monoidal category. If an object ''X'' has a left (resp. right) inverse ''X''−1 with respect to the tensor product then it is left (resp. right) rigid, and ''X'' * = ''X''−1. The operation of taking duals gives a contravariant functor on a rigid category. 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「rigid category」の詳細全文を読む スポンサード リンク
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