Dualizable and semi-flat objects in abstract module categories

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

Dualizable and semi-flat objects in abstract module categories. / Bak, Rune Harder.

I: Mathematische Zeitschrift, Bind 296, Nr. 1-2, 2020, s. 353-371.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bak, RH 2020, 'Dualizable and semi-flat objects in abstract module categories', Mathematische Zeitschrift, bind 296, nr. 1-2, s. 353-371. https://doi.org/10.1007/s00209-020-02501-z

APA

Bak, R. H. (2020). Dualizable and semi-flat objects in abstract module categories. Mathematische Zeitschrift, 296(1-2), 353-371. https://doi.org/10.1007/s00209-020-02501-z

Vancouver

Bak RH. Dualizable and semi-flat objects in abstract module categories. Mathematische Zeitschrift. 2020;296(1-2):353-371. https://doi.org/10.1007/s00209-020-02501-z

Author

Bak, Rune Harder. / Dualizable and semi-flat objects in abstract module categories. I: Mathematische Zeitschrift. 2020 ; Bind 296, Nr. 1-2. s. 353-371.

Bibtex

@article{e222e6ebb9ea4ad7bc804bd208bc0c2e,
title = "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.",
keywords = "Cotorsion pairs, Differential graded algebras and modules, Direct limit closure, Dualizable objects, Locally finitely presented categories, Semi-flat objects",
author = "Bak, {Rune Harder}",
year = "2020",
doi = "10.1007/s00209-020-02501-z",
language = "English",
volume = "296",
pages = "353--371",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer",
number = "1-2",

}

RIS

TY - JOUR

T1 - Dualizable and semi-flat objects in abstract module categories

AU - Bak, Rune Harder

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Cotorsion pairs

KW - Differential graded algebras and modules

KW - Direct limit closure

KW - Dualizable objects

KW - Locally finitely presented categories

KW - Semi-flat objects

UR - http://www.scopus.com/inward/record.url?scp=85084216507&partnerID=8YFLogxK

U2 - 10.1007/s00209-020-02501-z

DO - 10.1007/s00209-020-02501-z

M3 - Journal article

AN - SCOPUS:85084216507

VL - 296

SP - 353

EP - 371

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 1-2

ER -

ID: 242709059