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arXiv · 1503.06240

Categories of (co)isotropic linear relations

Alan Weinstein
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Abstract

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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Alan Weinstein. 2015-03-20. Categories of (co)isotropic linear relations. https://arxiv.org/abs/1503.06240

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