Percorrer por autor "Van der Linden, Tim"
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- Further remarks on the "Smith is Huq" conditionPublication . Martins-Ferreira, Nelson; Van der Linden, TimWe 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.
- A Note on the “Smith is Huq” ConditionPublication . Martins-Ferreira, Nelson; Van der Linden, TimWe 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.
- An observation on n-permutabilityPublication . Martins-Ferreira, Nelson; Rodelo, Diana; Van der Linden, TimWe 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.