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September 2019 Cotorsion pairs in categories of quiver representations
Henrik Holm, Peter Jørgensen
Kyoto J. Math. 59(3): 575-606 (September 2019). DOI: 10.1215/21562261-2018-0018

Abstract

We study the category Rep(Q,M) of representations of a quiver Q with values in an abelian category M. Under certain assumptions, we show that every cotorsion pair (A,B) in M induces two (explicitly described) cotorsion pairs (Φ(A),Rep(Q,B)) and (Rep(Q,A),Ψ(B)) in Rep(Q,M). This is akin to a result by Gillespie, which asserts that a cotorsion pair (A,B) in M induces cotorsion pairs (A˜,dgB˜) and (dgA˜,B˜) in the category Ch(M) of chain complexes in M. Special cases of our results recover descriptions of the projective and injective objects in Rep(Q,M) proved by Enochs, Estrada, and García Rozas.

Citation

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Henrik Holm. Peter Jørgensen. "Cotorsion pairs in categories of quiver representations." Kyoto J. Math. 59 (3) 575 - 606, September 2019. https://doi.org/10.1215/21562261-2018-0018

Information

Received: 17 October 2016; Revised: 30 March 2017; Accepted: 13 April 2017; Published: September 2019
First available in Project Euclid: 25 April 2019

zbMATH: 07108003
MathSciNet: MR3990178
Digital Object Identifier: 10.1215/21562261-2018-0018

Subjects:
Primary: 18E10
Secondary: 18G05, 18G15

Rights: Copyright © 2019 Kyoto University

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Vol.59 • No. 3 • September 2019
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