A convenient differential category
A convenient differential category
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发表时间：
2010
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通讯作者：
C. Tasson
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作者：
R. Blute;T. Ehrhard;C. Tasson
本文证明了麦基完备、分离的拓扑凸线形矢量空间和线形线性映射的范畴是一个微分范畴。这样的空间是由Frolicher和Kriegl引入的，他们称之为方便向量空间。虽然Frolicher和Kriegl的书中已经包含了证明这一观察所需的大部分结构，但我们在这里对方便向量空间的范畴给出了新的解释，作为Ehrhard和Regnier的微分线性逻辑的模型。与其将我们的证明建立在Frolicher和Kriegl提出的抽象范畴结构上，我们更倾向于关注方便向量空间的bornological结构。我们相信bornological结构最终将产生各种各样的微分逻辑模型。
In this paper, we show that the category of Mackey-complete, separated, topological convex bornological vector spaces and bornological linear maps is a differential category. Such spaces were introduced by Frolicher and Kriegl, where they were called convenient vector spaces. While much of the structure necessary to demonstrate this observation is already contained in Frolicher and Kriegl's book, we here give a new interpretation of the category of convenient vector spaces as a model of the differential linear logic of Ehrhard and Regnier. Rather than base our proof on the abstract categorical structure presented by Frolicher and Kriegl, we prefer to focus on the bornological structure of convenient vector spaces. We believe bornological structures will ultimately yield a wide variety of models of differential logics.