Homotopy cartesian diagrams in $n$-angulated categories

It has been proved by Bergh and Thaule that the higher mapping cone axiom is equivalent to the higher octahedral axiom for $n$-angulated categories. In this paper we use homotopy cartesian diagrams to give several new equivalent statements of the higher mapping cone axiom. As an application we give a new and elementary proof of the fact that the stable category of a Frobenius $(n-2)$-exact category is an $n$-angulated category, which was first proved by Jasso.

Keywords

$n$-angulated category, homotopy cartesian, mapping cone axiom, Frobenius $n$-exact category

2010 Mathematics Subject Classification

18E10, 18E30

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This work was partially supported by the Foundation of the Education Department of Fujian Province (Grant No. JZ160405) and Natural Science Foundation of China (Grant No. 11871014 and No. 11871259).

Received 15 July 2017

Received revised 23 February 2019

Published 5 June 2019