48 citations · 140 across the 46 of their papers we have counts for
8 papers · 1 filter
The morphism axiom for n-angulated categories
Emilie Arentz-Hansen, Petter Andreas Bergh, Marius Thaule
The morphism axiom for n-angulated categories states that a morphism between the bases of two n-angles can be extended to a morphism of n-angles. We show that this axiom is redunda…
Higher n-angulations from local rings
Petter Andreas Bergh, Gustavo Jasso, Marius Thaule
We show that the category of finitely generated free modules over certain local rings is n-angulated for every n at least 3. In fact, we construct several classes of n-angles, para…
The Grothendieck group of an n-angulated category
Petter Andreas Bergh, Marius Thaule
We define the Grothendieck group of an n-angulated category and show that for odd n its properties are as in the special case of n=3, i.e. the triangulated case. In particular, its…
The Gorenstein defect category
Petter Andreas Bergh, David A. Jorgensen, Steffen Oppermann
We consider the homotopy category of complexes of projective modules over a Noetherian ring. Truncation at degree zero induces a fully faithful triangle functor from the totally ac…
The axioms for n-angulated categories
Petter Andreas Bergh, Marius Thaule
We discuss the axioms for an n-angulated category, recently introduced by Geiss, Keller and Oppermann. In particular, we introduce a higher octahedral axiom, and show that it is eq…
Cluster tilting and complexity
Petter Andreas Bergh, Steffen Oppermann
We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one,…