RESEARCH ARTICLE

On the homotopy category of AC-injective complexes

  • James GILLESPIE
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  • Ramapo College of New Jersey, School of Theoretical and Applied Science, Mahwah, NJ 07430, USA

Received date: 08 Nov 2015

Accepted date: 07 Mar 2016

Published date: 01 Feb 2017

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Let R be any ring. We motivate the study of a class of chain complexes of injective R-modules that we call AC-injective complexes, showing that K(AC-Inj), the chain homotopy category of all AC-injective complexes, is always a compactly generated triangulated category. In general, all DGinjective complexes are AC-injective and in fact there is a recollement linking K(AC-Inj) to the usual derived category D(R). This is based on the author’s recent work inspired by work of Krause and Stovicek. Our focus here is on giving straightforward proofs that our categories are compactly generated.

Cite this article

James GILLESPIE . On the homotopy category of AC-injective complexes[J]. Frontiers of Mathematics in China, 2017 , 12(1) : 97 -115 . DOI: 10.1007/s11464-016-0551-x

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