Year: 2026
Type: preprint
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).
Source: arXiv (Cornell University)
Authors: Ma, Yajun, Yang, Peiru
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204913541
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