Dualizable and semi-flat objects in abstract module categories
Abstract
In this paper, we define what it means for an object in an abstract module category to be dualizable and we give a homological description of the direct limit closure of the dualizable objects. Our description recovers existing results of Govorov and Lazard, Oberst and R{\"o}hrl, and Christensen and Holm. When applied to differential graded modules over a differential graded algebra, our description yields that a DG-module is semi-flat if and only if it can be obtained as a direct limit of finitely generated semi-free DG-modules. We obtain similar results for graded modules over graded rings and for quasi-coherent sheaves over nice schemes.
Cite
@article{arxiv.1607.02609,
title = {Dualizable and semi-flat objects in abstract module categories},
author = {Rune Harder Bak},
journal= {arXiv preprint arXiv:1607.02609},
year = {2018}
}
Comments
19 pages. Final version to appear in Math. Z. Title have been slightly modified. Major changes in exposition. References have been added. Typos have been corrected. Main theorem strengthened