abstract: Differentiating an $n$-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 $n$-groupoid. As an immediate consequence we obtain that the tangent complex carries the structure of a Lie $n$-algebroid.

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@article{Li-Differentiating-L_infty-groupoids-2023,
 abstract = {Differentiating an $n$-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 $n$-groupoid.
As an immediate consequence we obtain that the tangent complex carries the
structure of a Lie $n$-algebroid.},
 arxiv = {arXiv:2309.00901},
 author = {Li,  Du and Ryvkin,  Leonid and Wessel,  Arne and Zhu,  Chenchang},
 doi = {10.1016/j.matpur.2026.103880},
 issn = {0021-7824},
 journal = {Journal de Mathématiques Pures et Appliquées},
 month = {March},
 pages = {103880},
 publisher = {Elsevier BV},
 title = {Differentiating $L_\infty$ groupoids},
 url = {http://dx.doi.org/10.1016/j.matpur.2026.103880},
 year = {2026}
}