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Abstract
Extriangulated categories were introduced by Nakaoka and Palu, which is a simultaneous generalization of exact categories and triangulated categories. Axiom (ET4) for extriangulated categories is an analogue of octahedron axiom (TR4) for triangulated categories. In this paper, we use homotopy cartesian squares in pre-extriangulated categories to investigate axiom (ET4). We provide several equivalent statements of axiom (ET4) and find out conditions under which the axiom is self-dual.
Acknowledgments
The authors sincerely thank the referee for careful reading and helpful comments and suggestions improving this paper.
Additional information
Funding
This work was supported by the Natural Science Foundation of Fujian Province (Grant No. 2020J01075).