2010/01/05 by Pohl, Anke D.
#22A22 (Primary) #57R18 #58H05 (Secondary) #Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1001.0668
It is well-known that reduced smooth orbifolds and proper effective foliation Lie groupoids form equivalent categories. However, for certain recent lines of research, equivalence of categories is not sufficient. We propose a notion of maps between reduced smooth orbifolds and a definition of a category in terms of marked proper effective étale Lie groupoids such that the arising category of orbifolds is isomorphic (not only equivalent) to this groupoid category.