PreprintCC BY 4.0arXiv
Ideal balanced pairs in n-exangulated categories
Abstract
This paper is devoted to ideal approximation theory in n-exangulated categories. We define ideal balanced pairs and explore their properties and equivalent characterizations. We prove that any complete ideal cotorsion triple (β,π¦,π₯) satisfying suitable assumptions yields an ideal balanced pair (β, π₯), and the converse holds under additional hypotheses. We further show that for an ideal balanced pair, it is equivalent to an additive subfunctor with enough projective morphisms and enough injective morphisms.
Related
BibTeX
@misc{zhang2026ideal,
title = {{Ideal balanced pairs in n-exangulated categories}},
author = {Peiyu Zhang and Zhuolin Zheng and Li Wang and Dajun Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28657},
eprint = {2610.28657},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28657},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ideal balanced pairs in n-exangulated categories
AU - Peiyu Zhang
AU - Zhuolin Zheng
AU - Li Wang
AU - Dajun Liu
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.28657
UR - https://arxiv.org/abs/2610.28657
AB - This paper is devoted to ideal approximation theory in n-exangulated categories. We define ideal balanced pairs and explore their properties and equivalent characterizations. We prove that any complete ideal cotorsion triple (β,π¦,π₯) satisfying suitable assumptions yields an ideal balanced pair (β, π₯), and the converse holds under additional hypotheses. We further show that for an ideal balanced pair, it is equivalent to an additive subfunctor with enough projective morphisms and enough injective morphisms.
ER -