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arXiv · 2112.06445

The (ET4) axiom for Extriangulated Categories

Xiaoxue Kong·Zengqiang Lin·Minxiong Wang
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Abstract

Extriangulated categories were introduced by Nakaoka and Palu, which is a simultaneous generalization of exact categories and triangulated categories. The axiom (ET4) for extriangulated categories is an analogue of the octahedron axiom (TR4) for triangulated categories. In this paper, we introduce homotopy cartesian squares in pre-extriangulated categories to investigate the axiom (ET4). We provide several equivalent statements of the axiom (ET4) and find out conditions under which the axiom is self-dual.

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Xiaoxue Kong, Zengqiang Lin, Minxiong Wang. 2021-12-13. The (ET4) axiom for Extriangulated Categories. https://arxiv.org/abs/2112.06445

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