The (ET4) axiom for Extriangulated Categories
Xiaoxue Kong, Zengqiang Lin, Minxiong Wang
TL;DR
This paper explores the (ET4) axiom in extriangulated categories, generalizing concepts from triangulated and exact categories, and investigates conditions for its self-duality using homotopy cartesian squares.
Contribution
It introduces homotopy cartesian squares in pre-extriangulated categories and provides equivalent formulations and conditions for the (ET4) axiom's self-duality.
Findings
Multiple equivalent statements of (ET4) are established.
Conditions for the self-duality of (ET4) are identified.
Homotopy cartesian squares are used to analyze the axiom.
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras