Integration of 2-term representations up to homotopy via 2-functors

Brahic, Olivier; Ortiz, Cristian

doi:10.1090/tran/7586

Integration of $2$-term representations up to homotopy via $2$-functors
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by Olivier Brahic and Cristian Ortiz PDF

Trans. Amer. Math. Soc. 372 (2019), 503-543 Request permission

Abstract:

Given a representation up to homotopy of a Lie algebroid on a $2$-term complex of vector bundles, we define the corresponding holonomy as a strict $2$-functor from a Weinstein path $2$-groupoid to the gauge $2$-groupoid of the underlying $2$-term complex. We construct a corresponding transformation $2$-groupoid, and we prove that the $1$-truncation of this $2$-groupoid is isomorphic to the Weinstein groupoid of the $\mathcal {VB}$-algebroid associated with a representation up to homotopy.

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