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2018•Homology Homotopy and ApplicationsOpen access

A note on homotopy categories of FP-injectives

Γεώργιος Δαλέζιος

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Abstract

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

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

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Available abstract

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

Key concepts: Subcategory, Homotopy category, Mathematics, Homotopy, Injective function, Model category, Pure mathematics, Characterization (materials science)

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