An observation on n-permutability

Martins-Ferreira, Nelson; Rodelo, Diana; Van der Linden, Tim

http://hdl.handle.net/10400.8/13444

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An observation on n-permutability.pdf	We 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.	106.47 KB	Adobe PDF	Download

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Authors

Martins-Ferreira, Nelson

Rodelo, Diana

Van der Linden, Tim

Abstract(s)

We 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.

Keywords

Mal’tsev category Goursat category n-permutable category pre-order equivalence relation internal category internal groupoid

URI

http://hdl.handle.net/10400.8/13444

Citation

Nelson 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.