# Constant Symplectic 2-groupoids

## TL;DR

This paper introduces the concept of constant symplectic 2-groupoids, establishing their classification and relationship with constant Courant algebroids and Dirac structures, advancing the understanding of higher symplectic geometry.

## Contribution

It defines symplectic 2-groupoids including those integrating Courant algebroids and classifies constant symplectic 2-groupoids via constant Courant algebroids.

## Key findings

- Constant symplectic 2-groupoids correspond to constant Courant algebroids.
- A correspondence exists between certain Dirac structures and Lagrangian sub-2-groupoids.
- The classification simplifies the understanding of symplectic 2-groupoids in the constant case.

## Abstract

We propose a definition of symplectic 2-groupoid which includes integrations of Courant algebroids that have been recently constructed. We study in detail the simple but illustrative case of constant symplectic 2-groupoids. We show that the constant symplectic 2-groupoids are, up to equivalence, in one-to-one correspondence with a simple class of Courant algebroids that we call constant Courant algebroids. Furthermore, we find a correspondence between certain Dirac structures and Lagrangian sub-2-groupoids.