| dbo:abstract |
In mathematics, the category of manifolds, often denoted Manp, is the category whose objects are manifolds of smoothness class Cp and whose morphisms are p-times continuously differentiable maps. This is a category because the composition of two Cp maps is again continuous and of class Cp. One is often interested only in Cp-manifolds modeled on spaces in a fixed category A, and the category of such manifolds is denoted Manp(A). Similarly, the category of Cp-manifolds modeled on a fixed space E is denoted Manp(E). One may also speak of the category of smooth manifolds, Man∞, or the category of analytic manifolds, Manω. (en) 数学の一分野である圏論において Cp-級多様体の圏（たようたいのけん、英: category of manifolds）Manp は、すべての Cp-級可微分多様体を対象とし、すべての Cp-級可微分写像（p-回連続的微分可能写像を射とする圏である。二つの Cp-級写像の合成はやはり Cp-級となるから、確かにこれで圏が得られている。 しばしば特定の圏 A に属する対象をモデルに持つ多様体（A における多様体対象）のみを考えたいという場合が生じる。そのような限定された意味の多様体の成す圏は Manp(A) のように書き表す。同様に特定の空間 E の上で定められる多様体の成す圏を Manp(E) と書く。 滑らかな多様体の圏 Man∞ やの圏 Manω も同様に考えられる。 (ja) |
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https://archive.org/details/introductiontoma00lwtu_506 |
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| rdfs:comment |
数学の一分野である圏論において Cp-級多様体の圏（たようたいのけん、英: category of manifolds）Manp は、すべての Cp-級可微分多様体を対象とし、すべての Cp-級可微分写像（p-回連続的微分可能写像を射とする圏である。二つの Cp-級写像の合成はやはり Cp-級となるから、確かにこれで圏が得られている。 しばしば特定の圏 A に属する対象をモデルに持つ多様体（A における多様体対象）のみを考えたいという場合が生じる。そのような限定された意味の多様体の成す圏は Manp(A) のように書き表す。同様に特定の空間 E の上で定められる多様体の成す圏を Manp(E) と書く。 滑らかな多様体の圏 Man∞ やの圏 Manω も同様に考えられる。 (ja) In mathematics, the category of manifolds, often denoted Manp, is the category whose objects are manifolds of smoothness class Cp and whose morphisms are p-times continuously differentiable maps. This is a category because the composition of two Cp maps is again continuous and of class Cp. One is often interested only in Cp-manifolds modeled on spaces in a fixed category A, and the category of such manifolds is denoted Manp(A). Similarly, the category of Cp-manifolds modeled on a fixed space E is denoted Manp(E). (en) |
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Category of manifolds (en) 多様体の圏 (ja) |
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