Dualizable and semi-flat objects in abstract module categories
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- DUALIZABLE AND SEMI-FLAT OBJECTS IN ABSTRACT
Accepted author manuscript, 294 KB, PDF document
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 Röhrl, 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.
Original language | English |
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Journal | Mathematische Zeitschrift |
Volume | 296 |
Issue number | 1-2 |
Pages (from-to) | 353-371 |
ISSN | 0025-5874 |
DOIs | |
Publication status | Published - 2020 |
- Cotorsion pairs, Differential graded algebras and modules, Direct limit closure, Dualizable objects, Locally finitely presented categories, Semi-flat objects
Research areas
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