PreprintCC BY 4.0arXiv
On derived equivalences of exact structures on the category of representations k[x]/(xn)
Abstract
From the perspective of homological algebra, exact categories are interesting because they possess derived categories. Typically, an additive category admits many exact structures. If the original category is sufficiently nice (for example, quasi-abelian), a classification of exact structures can be given in terms of certain Serre subcategories in the category of contravariant functors. It turns out that the derived categories of different exact structures are functorially related. This work is concerned with sufficient conditions for the derived equivalence of different exact structures on certain categories.
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BibTeX
@misc{monchenko2026derived,
title = {{On derived equivalences of exact structures on the category of representations $k[x]/(x^n)$}},
author = {Nikita Monchenko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34363},
eprint = {2610.34363},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34363},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On derived equivalences of exact structures on the category of representations k[x]/(x^n)
AU - Nikita Monchenko
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34363
UR - https://arxiv.org/abs/2610.34363
AB - From the perspective of homological algebra, exact categories are interesting because they possess derived categories. Typically, an additive category admits many exact structures. If the original category is sufficiently nice (for example, quasi-abelian), a classification of exact structures can be given in terms of certain Serre subcategories in the category of contravariant functors. It turns out that the derived categories of different exact structures are functorially related. This work is concerned with sufficient conditions for the derived equivalence of different exact structures on certain categories.
ER -