Martins-Ferreira, NelsonRodelo, DianaVan der Linden, Tim2025-06-272025-06-272014-05Nelson Martins-Ferreira, Diana Rodelo, Tim Van der Linden "An observation on n-permutability," Bulletin of the Belgian Mathematical Society - Simon Stevin, Bull. Belg. Math. Soc. Simon Stevin 21(2), 223-230, (may 2014). DOI: https://doi.org/10.36045/bbms/1400592620.1370-1444http://hdl.handle.net/10400.8/13444We prove that in a regular category all reflexive and transitive relations are symmetric if and only if every internal category is an internal groupoid. In particular, these conditions hold when the category is n-permutable for some n.engMal’tsev categoryGoursat categoryn-permutable categorypre-orderequivalence relationinternal categoryinternal groupoidjournal article10.36045/bbms/1400592620