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arXiv · 2610.16403

Ideal quotients of $n$-exact categories

Weikang Weng
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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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Weikang Weng. 2026-10-12. Ideal quotients of $n$-exact categories. https://arxiv.org/abs/2610.16403

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