Frontiers of Mathematics in China >
On the homotopy category of AC-injective complexes
Received date: 08 Nov 2015
Accepted date: 07 Mar 2016
Published date: 01 Feb 2017
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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.
Key words： AC-injective; recollement; compactly generated; triangulated category
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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