It was recently proved that every additive category has a unique maximal exact structure, while it remained open whether the distinguished short exact sequences of this canonical exact structure coincide with the stable short exact sequences. The question is answered by a counterexample which shows that none of the steps to construct the maximal exact structure can be dropped.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-7,
author = {Wolfgang Rump},
title = {Stable short exact sequences and the maximal exact structure of an additive category},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {87-96},
zbl = {1318.18005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-7}
}
Wolfgang Rump. Stable short exact sequences and the maximal exact structure of an additive category. Fundamenta Mathematicae, Tome 228 (2015) pp. 87-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-7/