abstract: Tepui groupoids are a generalization of Lie groupoids which allow the arrow space to be singular, as is the case for holonomy groupoids of singular foliations. We construct a Lie differentiation functor for a large class of tepui groupoids. When restricted to effective and source-connected tepui groupoids, this differentiation recovers the correspondence between holonomy groupoids and their underlying singular foliations.

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@misc{Garmendia-Differentiation-of-tepui-2026,
 abstract = {Tepui groupoids are a generalization of Lie groupoids which allow the arrow space to be singular, as is the case for holonomy groupoids of singular foliations. We construct a Lie differentiation functor for a large class of tepui groupoids. When restricted to effective and source-connected tepui groupoids, this differentiation recovers the correspondence between holonomy groupoids and their underlying singular foliations.},
 archiveprefix = {arXiv},
 author = {Garmendia, Alfonso and Miyamoto, David and Ryvkin, Leonid},
 eprint = {2611.08825},
 primaryclass = {math.DG},
 title = {Differentiation of tepui groupoids and the holonomy groupoid of singular foliations},
 url = {https://arxiv.org/abs/2611.08825},
 year = {2026}
}