Year: 2026
Type: preprint
Abstract: Fu, Guil Asensio, Herzog and Torrecillas asked whether a complete ideal cotorsion pair of object ideals in an exact category always induces a complete cotorsion pair of objects. We show that it need not, even in a Hom-finite, weakly idempotent complete Frobenius exact category. Our example consists of bounded complexes of finite-dimensional vector spaces with even total cohomology dimension. We characterize special object approximations by parity and identify the obstruction as a non-split idempotent in the stable category. For cohereditary pairs, a criterion of Saor\'ın and Šťov\'ıček gives an affirmative answer when the stable category is idempotent complete.
Source: arXiv (Cornell University)
Authors: Ren, Junpeng, Wang, Yucheng
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213498370