A note on the "Smith is Huq" condition

Martins-Ferreira, Nelson;Van der Linden, Tim
(2012) Applied Categorical Structures : a journal devoted to applications of categorical methods in algebra, analysis, order, topology and computer science — Vol. 20, n° 2, p. 175-187 (2012)

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Abstract
We show that two known conditions which arose naturally in commutator theory and in the theory of internal crossed modules coincide: every star-multiplicative graph is multiplicative if and only if every two effective equivalence relations commute as soon as their normalisations do. This answers a question asked by George Janelidze.
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Martins-Ferreira, N., & Van der Linden, T. (2012). A note on the “Smith is Huq” condition. Applied Categorical Structures : a journal devoted to applications of categorical methods in algebra, analysis, order, topology and computer science, 20(2), 175-187. https://doi.org/10.1007/s10485-010-9231-2 (Original work published 2012)