Open Access
may 2014 An observation on $n$-permutability
Nelson Martins-Ferreira, Diana Rodelo, Tim Van der Linden
Bull. Belg. Math. Soc. Simon Stevin 21(2): 223-230 (may 2014). DOI: 10.36045/bbms/1400592620


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 $n$.


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Nelson Martins-Ferreira. Diana Rodelo. Tim Van der Linden. "An observation on $n$-permutability." Bull. Belg. Math. Soc. Simon Stevin 21 (2) 223 - 230, may 2014.


Published: may 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1301.08014
MathSciNet: MR3211011
Digital Object Identifier: 10.36045/bbms/1400592620

Primary: 08C05 , 18B99 , 18C10 , 18E10

Keywords: $n$-permutable category , equivalence relation , Goursat category , internal category , internal groupoid , Mal'tsev category , preorder

Rights: Copyright © 2014 The Belgian Mathematical Society

Vol.21 • No. 2 • may 2014
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