A note on homotopy categories of FP-Injectives

2018/03/03 by Dalezios, Georgios
#18E30 (Primary) 16E35 #18G25 (Secondary) #Category Theory (math.CT) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1803.01140

Abstract

For a locally finitely presented Grothendieck category A, we consider a certain subcategory of the homotopy category of FP-injective objects in A which we show is compactly generated. In the case where A is locally coherent, we identify this subcategory with the derived category of FP-injective objects in A. Our results are, in a sense, dual to the ones obtained by Neeman on the homotopy category of flat modules. Our proof is based on extending a characterization of the pure acyclic complexes which is due to Emmanouil.

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