Differentiating $L_\infty$ groupoids
Differential Geometry
2026-02-18 v3
Abstract
Differentiating an Lie -groupoid via the differential-geometric fat point a priori only yielads a presheaf of graded manifolds. In this article we prove that this presheaf is representable by the tangent complex of the Lie -groupoid. As an immediate consequence we obtain that the tangent complex carries the structure of a Lie -algebroid.
Keywords
Cite
@article{arxiv.2309.00901,
title = {Differentiating $L_\infty$ groupoids},
author = {Du Li and Leonid Ryvkin and Arne Wessel and Chenchang Zhu},
journal= {arXiv preprint arXiv:2309.00901},
year = {2026}
}
Comments
34 pages, to appear in JMPA