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The homotopy category of acyclic complexes of pure-projective modules (2201.05542v2)
Published 14 Jan 2022 in math.AT, math.CT, and math.RA
Abstract: Let $R$ be any ring with identity. We show that the homotopy category of all acyclic chain complexes of pure-projective $R$-modules is a compactly generated triangulated category. We do this by constructing abelian model structures that put this homotopy category into a recollement with two other compactly generated triangulated categories: The usual derived category of $R$ and the pure derived category of $R$. This also gives a new model for the derived category.