@article{Iglesias-zemmour2025, 
author = {Patrick Iglesias-zemmour},
title = {Groupoids in diffeology},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {12},
pages = {7957-7973},
keywords = {diffeology, diffeological groupoid, stratification, Klein groupoid, orbifolds, quasifolds, noncommutative geometry, geometric quantization},
url = {https://www.sciopen.com/article/10.3934/era.2025350},
doi = {10.3934/era.2025350},
abstract = {This expository paper recounts the development and application of the concept of a diffeological groupoid, from its introduction in 1985 to its use in current research. We demonstrate how this single concept has served as a powerful and unifying tool for defining fundamental structures, analyzing the stratification of complex spaces like orbifolds, building a bridge to noncommutative geometry, and, most recently, forging new approaches to geometric quantization. The paper aims to provide a cohesive narrative of this journey, making explicit certain concepts like the "Klein groupoid" and showcasing the enduring vitality of the diffeological groupoid in modern geometry and physics.}
}