# nLab super-groupoid

### Context

#### Cohesive $\infty$-Toposes

cohesive topos

cohesive (∞,1)-topos

cohesive homotopy type theory

## Structures in a cohesive $(\infty,1)$-topos

structures in a cohesive (∞,1)-topos

## Structures with infinitesimal cohesion

infinitesimal cohesion?

supersymmetry

# Contents

## Definition

A supergroupoid is a 1-truncated super ∞-groupoid.

## Examples

• For $\mathfrak{g}$ a super Lie algebra and $X$ a smooth manifold, the groupoid of Lie-algebra valued forms $\Omega^1(X, \mathfrak{g})$ is a super-groupoid: over a given superpoint $\mathbb{R}^{0|q}$ with function algebra the Grassmann algebra $\Lambda_q$ it assigns the ordinary groupoid of Lie-algebra valued forms of the ordinary Lie algebra $(\mathfrak{g} \otimes \Lambda_q)_{even}$:

$\Omega^1(X, \mathfrak{g}) : \mathbb{R}^{0|q} \mapsto \Omega^1(X, (\mathfrak{g} \otimes \Lambda_q)_{even}) \,.$
Created on April 20, 2011 22:16:00 by Urs Schreiber (131.211.239.58)