The axioms for n–angulated categories

Bergh, Petter Andreas; Thaule, Marius

doi:10.2140/agt.2013.13.2405

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The axioms for $n$–angulated categories

Petter Andreas Bergh and Marius Thaule

Algebraic & Geometric Topology 13 (2013) 2405–2428

DOI: 10.2140/agt.2013.13.2405

Abstract

We discuss the axioms for an $n$ –angulated category, recently introduced by Geiss, Keller and Oppermann in [J. Reine Angew. Math. 675 (2013) 101–120]. In particular, we introduce a higher “octahedral axiom”, and show that it is equivalent to the mapping cone axiom for an $n$ –angulated category. For a triangulated category, the mapping cone axiom, our octahedral axiom and the classical octahedral axiom are all equivalent.

Keywords

triangulated categories, $n$–angulated categories, octahedral axiom

Mathematical Subject Classification 2010

Primary: 18E30

References

Publication

Received: 18 November 2012

Revised: 8 March 2013

Accepted: 12 March 2013

Published: 2 July 2013

Authors

Petter Andreas Bergh
Department of Mathematical Sciences NTNU NO-7491 Trondheim Norway
http://www.math.ntnu.no/~bergh/
Marius Thaule
Department of Mathematical Sciences NTNU NO-7491 Trondheim Norway
http://www.math.ntnu.no/~mariusth/

Volume 13, issue 4 (2013)