Orbifolds as a localization of the 2-category of groupoids
Differential Geometry
2010-09-02 v3 Category Theory
Abstract
We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category structure drops down to the localization. In our construction the spaces of 1- and 2-arrows admit natural topologies, the space of morphisms (1-arrows) between two orbifolds is naturally a groupoid and the symmetries of an orbifold form a strict 2-group.
Cite
@article{arxiv.math/0608396,
title = {Orbifolds as a localization of the 2-category of groupoids},
author = {Eugene Lerman},
journal= {arXiv preprint arXiv:math/0608396},
year = {2010}
}
Comments
This paper has been withdrawn by the author