Orbifolds and groupoids
Algebraic Topology
2010-10-05 v1 Algebraic Geometry
Abstract
We define a 2-category structure (Pre-Orb) on the category of reduced complex orbifold atlases. We construct a 2-functor F from (Pre-Orb) to the 2-category (Grp) of proper \'etale effective groupoid objects over the complex manifolds. Both on (Pre-Orb) and (Grp) there are natural equivalence relations on objects: (a natural extension of) equivalence of orbifold atlases in (Pre-Orb) and Morita equivalences in (Grp). We prove that F induces a bijection between the equivalence classes of its source and target.
Cite
@article{arxiv.1008.0988,
title = {Orbifolds and groupoids},
author = {Matteo Tommasini},
journal= {arXiv preprint arXiv:1008.0988},
year = {2010}
}