On thick subcategories of the category of projective presentations
Representation Theory
2023-08-23 v3
Abstract
We study thick subcategories of the category of 2-term complexes of projective modules over an associative algebra. We show that those thick subcategories that have enough injectives are in explicit bijection with 2-term silting complexes and complete cotorsion pairs. We also provide a bijection with left finite wide subcategories of the module category and prove that all these maps are compatible with previously known correspondences. We discuss possible applications to stability conditions.
Keywords
Cite
@article{arxiv.2303.05226,
title = {On thick subcategories of the category of projective presentations},
author = {Monica Garcia},
journal= {arXiv preprint arXiv:2303.05226},
year = {2023}
}
Comments
35 pages V2: typos corrected V3: new introduction for section 4, typos corrected