nLab
super-groupoid

Definition

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

Examples

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

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