Differentiating $L_{\infty }$ groupoids

Abstract

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

34 pages, to appear in JMPA