K‐flat complexes and derived categories

Let R $R$ be a ring with identity. Inspired by recent work in Emmanouil, Preprint, 2021, we show that the derived category of is equivalent to chain homotopy all K-flat complexes pure-injective components. This implicitly related recollement exhibit. It expresses D p u r ( ) $\mathcal {D}_{pur}(R)$ , pure as an attachment usual {D}(R)$ Emmanouil's quotient K − f l t : = / F {D}_{\textnormal {K-flat}}(R):=K(R)/K\textnormal {-Flat}$ which call here category. follows this Verdier compactly generated triangulated We obtain our results using methods cotorsion pairs construct (cofibrantly generated) monoidal abelian model structures on exact along degreewise structure. In fact, most are obtained corollaries general method associates structure any class so-called C {C}$ -acyclic complexes, where given complexes. Finally, also give new characterization terms .