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The axioms for $n$–angulated categories

Petter Andreas Bergh and Marius Thaule

Algebraic & Geometric Topology 13 (2013) 2405–2428
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/