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Further remarks on the "Smith is Huq" condition

Publication . Martins-Ferreira, Nelson; Van der Linden, Tim

We compare the Smith is Huq condition (SH) with three commutator conditions in semi-abelian categories: first an apparently weaker condition which arose in joint work with Bourn and turns out to be equivalent with (SH), then an apparently equivalent condition which takes commutation of non-normal subobjects into account and turns out to be stronger than (SH). This leads to the even stronger condition that weighted commutators in the sense of Gran, Janelidze and Ursini are independent of the chosen weight, which is known to be false for groups but turns out to be true in any two-nilpotent semi-abelian category.

2015-08Journal article

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On Algebraic and More General Categories Whose Split Epimorphisms Have Underlying Product Projections

Publication . Gray, J. R. A.; Martins-Ferreira, Nelson

We characterize those varieties of universal algebras where every split epimorphism considered as a map of sets is a product projection. In addition we obtain new characterizations of semi-abelian, protomodular, unital and subtractive varieties as well as varieties of right Ω-loops and biternary systems.

2015-06Journal article

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