A note on the Wehrheim-Woodward category
Symplectic Geometry
2011-03-14 v2 Category Theory
Abstract
Wehrheim and Woodward have shown how to embed all the canonical relations between symplectic manifolds into a category in which the composition is the usual one when transversality and embedding assumptions are satisfied. A morphism in their category is an equivalence class of composable sequences of canonical relations, with composition given by concatenation. In this note, we show that every such morphism is represented by a sequence consisting of just two relations, one of them a reduction and the other a coreduction.
Cite
@article{arxiv.1012.0105,
title = {A note on the Wehrheim-Woodward category},
author = {Alan Weinstein},
journal= {arXiv preprint arXiv:1012.0105},
year = {2011}
}
Comments
11 pages, to appear in Journal of Geometric Mechanics special issue in honor of Tudor Ratiu's 60'th birthday. Minor revisions in second version