nLab super-groupoid

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 $(\mathfrak{g} \otimes \Lambda_q)_{even}$:

  $$\Omega^1(X, \mathfrak{g}) : \mathbb{R}^{0|q} \mapsto \Omega^1(X, (\mathfrak{g} \otimes \Lambda_q)_{even}) \,.$$