Categorical Methods in Non Abelian Algebra

Publications

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

Restricted access

An observation on n-permutability

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

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.

2014-05Journal article

Open access