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Licensed Unlicensed Requires Authentication Published by De Gruyter February 21, 2014

On a question of Gillespie

  • Xiaoyan Yang EMAIL logo and Nanqing Ding
From the journal Forum Mathematicum

Abstract

A question of Gillespie concerning the completeness of the induced cotorsion pairs is settled in the general setting of any bicomplete abelian category. That is, given a complete hereditary cotorsion pair (𝒜,) in a bicomplete abelian category, we show that the cotorsion pairs of chain complexes (𝒜˜,dg˜) and (dg𝒜˜,˜) are complete, compatible and hereditary. This immediately puts a model structure on the chain complex category. As an application of this result, we establish homological dimensions of unbounded complexes in a Grothendieck category by means of dg𝒜 complexes and dg complexes respectively. Some examples of complete hereditary cotorsion pairs in Grothendieck categories are given.

Funding source: NSFC

Award Identifier / Grant number: 11371187

Funding source: NSFC

Award Identifier / Grant number: 11361051

Funding source: NSF of Jiangsu Province of China

Award Identifier / Grant number: BK2011068

Funding source: China Postdoctoral Science Foundation

Award Identifier / Grant number: 2012M511713

Funding source: PAPD

We wish to thank the referee for the very helpful suggestions which have been incorporated herein.

Received: 2013-1-25
Revised: 2013-8-22
Published Online: 2014-2-21
Published in Print: 2015-11-1

© 2015 by De Gruyter

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