A Note on the “Smith is Huq” Condition

Martins-Ferreira, NelsonVan der Linden, Tim2026-01-152026-01-152010-07-07Martins-Ferreira, N., Van der Linden, T. A Note on the “Smith is Huq” Condition. Appl Categor Struct 20, 175–187 (2012). https://doi.org/10.1007/s10485-010-9231-20927-28521572-9095http://hdl.handle.net/10400.8/15348We show that two known conditions which arose naturally in commutator theory and in the theory of internal crossed modules coincide: every starmultiplicative graph is multiplicative if and only if every two ef fective equivalence relations commute as soon as their normalisations do. This answers a question asked by George Janelidze.engCommutatorInternal reflexive graphStar-multiplicationGroupoidProtomodular categorySemi-abelian categoryA Note on the “Smith is Huq” Conditionjournal article10.1007/s10485-010-9231-2