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.
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