Model structures on the category of Q-shaped modules
Abstract
We develop a method for constructing abelian model structures on the category Q,AMod of Q-shaped modules from cotorsion pairs in AMod, where Q is a small preadditive category satisfying certain conditions and AMod denotes the category of left A-modules for any ring A. More precisely, we construct two cotorsion pairs in Q,AMod from a given cotorsion pair in AMod. This leads to a construction of projective model structures on Q,AMod under the condition that Q has no cycles. We further apply this method to the category Dif(A) of differential left A-modules, viewed as a category of Q-shaped modules for a suitable choice of Q. In this case, the induced cotorsion pairs are shown to be compatible, thereby giving rise to abelian model structures on Dif(A).
Related
- One-periodic category of twisted complexes, Cohen-Macaulay modules and differential modules
- Acyclic and totally acyclic objects in the Q-shaped derived category
- Finitistic dimension via modules over the singularity category
- On the Stable category of maximal Cohen-Macaulay modules over Gorenstein rings-II
- Weight structures and t-structures on the triangulated category generated by a ℙ-object
BibTeX
@misc{ma2026model,
title = {{Model structures on the category of Q-shaped modules}},
author = {Yajun Ma and Peiru Yang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29267},
eprint = {2608.29267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29267},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Model structures on the category of Q-shaped modules
AU - Yajun Ma
AU - Peiru Yang
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29267
UR - https://arxiv.org/abs/2608.29267
AB - We develop a method for constructing abelian model structures on the category Q,AMod of Q-shaped modules from cotorsion pairs in AMod, where Q is a small preadditive category satisfying certain conditions and AMod denotes the category of left A-modules for any ring A. More precisely, we construct two cotorsion pairs in Q,AMod from a given cotorsion pair in AMod. This leads to a construction of projective model structures on Q,AMod under the condition that Q has no cycles. We further apply this method to the category Dif(A) of differential left A-modules, viewed as a category of Q-shaped modules for a suitable choice of Q. In this case, the induced cotorsion pairs are shown to be compatible, thereby giving rise to abelian model structures on Dif(A).
ER -