Ideal quotients of n-exact categories
Abstract
In this paper, we extend the notion of a removable subcategory to n-exact categories, and prove that an ideal quotient by a subcategory of projective-injectives inherits an n-exact structure from the original category if and only if the subcategory is removable. In the Frobenius case, the quotient remains Frobenius, and the stable (n+2)-angulated categories are equivalent. We give a sufficient condition for a subcategory of projective-injectives to be removable. We also show that the ideal quotient construction is compatible with cluster tilting. Finally, we apply the construction to $2$-cluster tilting subcategories of the category of ACM bundles on a Geigle--Lenzing projective plane, obtaining quotients for both natural and relative $2$-exact structures.
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BibTeX
@misc{weng2026ideal,
title = {{Ideal quotients of $n$-exact categories}},
author = {Weikang Weng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16403},
eprint = {2610.16403},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16403},
}
RIS
TY - UNPB
TI - Ideal quotients of n-exact categories
AU - Weikang Weng
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16403
UR - https://arxiv.org/abs/2610.16403
AB - In this paper, we extend the notion of a removable subcategory to n-exact categories, and prove that an ideal quotient by a subcategory of projective-injectives inherits an n-exact structure from the original category if and only if the subcategory is removable. In the Frobenius case, the quotient remains Frobenius, and the stable (n+2)-angulated categories are equivalent. We give a sufficient condition for a subcategory of projective-injectives to be removable. We also show that the ideal quotient construction is compatible with cluster tilting. Finally, we apply the construction to $2$-cluster tilting subcategories of the category of ACM bundles on a Geigle--Lenzing projective plane, obtaining quotients for both natural and relative $2$-exact structures.
ER -