Further remarks on the "Smith is Huq" condition

Martins-Ferreira, Nelson; Van der Linden, Tim

http://hdl.handle.net/10400.8/13339

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Authors

Martins-Ferreira, Nelson

Van der Linden, Tim

Abstract(s)

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.

Keywords

Arithmetical category Basic fibration Fibration of points Higgins commutator Huq commutator Semi-abelian category Smith commutator Weighted commutator

URI

http://hdl.handle.net/10400.8/13339

Citation

Martins-Ferreira, N., Van der Linden, T. Further Remarks on the “Smith is Huq” Condition. Appl Categor Struct 23, 527–541 (2015). https://doi.org/10.1007/s10485-014-9368-5