A note on homotopy categories of FP-injectives

For a locally finitely presented Grothendieck category A, we consider a certain subcategory of the homotopy category of FP-injectives 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-injectives 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.