Morita equivalence of shifted symplectic Lie n-groupoids

Symplectic structures on higher objects like Lie groupoids have been studied for some time now, but not all of the proposed definitions are preserved under Morita equivalence of Lie groupoids, in turn giving rise to a consistent notion of symplectic stacks. Recently, this concept has been generalized to m -shifted symplectic forms on Lie n -groupoids, which are indeed preserved under Morita equivalence of Lie n -groupoids. In this paper, we give a rigorous proof for this statement.

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Journal
Differential Geometry and its Applications
Published
2026-10-28
DOI
https://doi.org/10.1016/j.difgeo.2026.102453
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
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Morita equivalence of shifted symplectic Lie n-groupoids

Milena Weiershausen
1 links
Differential Geometry and its Applications
Homotopy and Cohomology in Algebraic Topology
article

Morita equivalence of shifted symplectic Lie n-groupoids

Milena Weiershausen
article en

Abstract

Symplectic structures on higher objects like Lie groupoids have been studied for some time now, but not all of the proposed definitions are preserved under Morita equivalence of Lie groupoids, in turn giving rise to a consistent notion of symplectic stacks. Recently, this concept has been generalized to m -shifted symplectic forms on Lie n -groupoids, which are indeed preserved under Morita equivalence of Lie n -groupoids. In this paper, we give a rigorous proof for this statement.

Differential Geometry and its ApplicationsVol. 105
University of Göttingen (DE)
Openalex Percentile: Top 7%
Homotopy and Cohomology in Algebraic Topology
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