Double groupoids and $2$-groupoids in regular Mal'tsev categories

Nadja Egner, Marino Gran

We prove that the category 2-$\mathrm{Grpd}(\mathcal{C})$ of internal $2$-groupoids is a Birkhoff subcategory of the category ${\mathrm{Grpd}}^2(\mathcal{C})$ of double groupoids…