PreprintCC0arXiv
Pretriangulated categories failing (TR4)
Abstract
We introduce gemstones in a pretriangulated category, which are used to perturb pretriangulated structures. For a triangulated category π― whose stable category of coherent functors admits a gemstone, we construct pretriangulated structures on π― which fail the octahedral axiom (TR4). This confirms a long-standing conjecture on triangulated categories.
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BibTeX
@misc{chen2026pretriangulated,
title = {{Pretriangulated categories failing (TR4)}},
author = {Xiao-Wu Chen and Sergei O. Ivanov and Jian Liu and Xue-Song Lu and Vladimir Sosnilo and Chencheng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.09777},
eprint = {2608.09777},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.09777},
note = {CC0},
}
RIS
TY - UNPB
TI - Pretriangulated categories failing (TR4)
AU - Xiao-Wu Chen
AU - Sergei O. Ivanov
AU - Jian Liu
AU - Xue-Song Lu
AU - Vladimir Sosnilo
AU - Chencheng Zhang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2608.09777
UR - https://arxiv.org/abs/2608.09777
AB - We introduce gemstones in a pretriangulated category, which are used to perturb pretriangulated structures. For a triangulated category π― whose stable category of coherent functors admits a gemstone, we construct pretriangulated structures on π― which fail the octahedral axiom (TR4). This confirms a long-standing conjecture on triangulated categories.
ER -