An observation on n-permutability

Martins-Ferreira, Nelson;Rodelo, Diana;Van der Linden, Tim
(2014) Belgian Mathematical Society - Simon Stevin. Bulletin — Vol. 21, n° 2, p. 223-230 (2014)

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  • Martins-Ferreira, NelsonInstituto Politecnico de Leiria
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  • Rodelo, DianaUniversidade do Algarve
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  • Van der Linden, Timorcid-logoUCLouvain
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Abstract
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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Martins-Ferreira, N., Rodelo, D., & Van der Linden, T. (2014). An observation on n-permutability. Belgian Mathematical Society - Simon Stevin. Bulletin, 21(2), 223-230. https://hdl.handle.net/2078.5/60569 (Original work published 2014)