Journal of Symplectic Geometry

Volume 15 (2017)

Number 2

Categories of (co)isotropic linear relations

Pages: 603 – 620



Alan Weinstein (Department of Mathematics, University of California at Berkeley)


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 form a free submonoid with two generators in the additive monoid of pairs of nonnegative integers.

Received 28 March 2015

Published 26 July 2017