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arXiv · 2609.00602

A right pretriangulated category which is not right triangulated

Jing He·Panyue Zhou
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Abstract

Chen, Liu, Lu, and Zhang recently constructed a pretriangulated category with invertible suspension in which Verdier's octahedral axiom fails. We introduce a general enlargement construction for right pretriangulated categories and show that it preserves axioms (RTR1)-(RTR3), while failure of (RTR4) is detected by the forgetful functor. Applied to their type $A_5$ example, the construction yields a right pretriangulated category that is not right triangulated. In this example, the suspension is faithful but not essentially surjective.

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BibTeXRIS

Jing He, Panyue Zhou. 2026-09-01. A right pretriangulated category which is not right triangulated. https://arxiv.org/abs/2609.00602

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