Categories of (co)isotropic linear relations
Symplectic Geometry
2015-03-24 v1 Category Theory
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.
Cite
@article{arxiv.1503.06240,
title = {Categories of (co)isotropic linear relations},
author = {Alan Weinstein},
journal= {arXiv preprint arXiv:1503.06240},
year = {2015}
}