Categories of (co)isotropic linear relations

DOI10.4310/JSG.2017.V15.N2.A5zbMath1388.18002arXiv1503.06240MaRDI QIDQ1689658

Peng Zhang

Publication date: 17 January 2018

Published in: The Journal of Symplectic Geometry (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1503.06240

zbMATH Keywords

transversalitycongenial paircongenial triplecotangent functordefect of the pair (sequence)excess of a sequencehighly selective categoryselective categoryselective functorshadow functorWehrheim and Woodward categories

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Geometry and quantization, symplectic methods (81S10) Basic linear algebra (15A99) Categories of spans/cospans, relations, or partial maps (18B10)

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