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Cotorsion Pairs in Categories of Quiver Representations

Lookup NU author(s): Professor Peter Jorgensen

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Abstract

ABSTRACT. We study the category Rep(Q;M) of representations of a quiver Q with values in an abelian categoryM. Under certain assumptions, we show that every cotorsion pair (A;B) in M induces two (explicitly described) cotorsion pairs (F(A);Rep(Q;B)) and (Rep(Q;A);Y(B)) in Rep(Q;M). This is akin to a result by Gillespie, which asserts that a cotorsion pair (A;B) inMinduces cotorsion pairs (Ae;dgBe) and (dgAe;Be) in the category Ch(M) of chain complexes inM. Special cases of our results recover descriptions of the projective and injective objects in Rep(Q;M) proved by Enochs, Estrada, and Rozas.Garc´ıa Rozas.


Publication metadata

Author(s): Holm H, Jorgensen P

Publication type: Article

Publication status: Published

Journal: Kyoto Journal of Mathematics

Year: 2019

Volume: 59

Issue: 3

Pages: 575-606

Online publication date: 25/04/2019

Acceptance date: 13/04/2017

Date deposited: 10/05/2017

ISSN (print): 2156-2261

ISSN (electronic): 2154-3321

Publisher: Duke University Press

URL: https://doi.org/10.1215/21562261-2018-0018

DOI: 10.1215/21562261-2018-0018


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