（余）迷向线性关系范畴

摘要：

在有限维向量空间之间的线性关系范畴中，复合仅在满足横截性和幺正性条件的关系对上表现良好。Wehrheim和Woodward的建构使得在保留范畴结构的同时强加这些条件成为可能。我们分析的情况下，所有的线性关系，以及（共）各向同性关系的辛向量空间的类别。在每种情况下，Wehrheim-Woodward范畴都是原始关系范畴通过单位对象的自同态的中心扩张，单位对象是非负整数对的加法幺半群中具有两个生成元的自由子幺半群。

英文摘要：

In categories of linear relations between finite dimensional vector spaces, composition is well-behaved only at pairs of relations satisfying transversality and monicity conditions. A construction of Wehrheim and Woodward makes it possible to impose these conditions while retaining the structure of a category. We analyze the resulting category in the case of all linear relations, as well as for (co)isotropic relations between symplectic vector spaces. In each case, the Wehrheim-Woodward category is a central extension of the original category of relations by the endomorphisms of the unit object, which is a free submonoid with two generators in the additive monoid of pairs of nonnegative integers.

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