Cotorsion pairs in \(\mathbf{C}(R-\text{Mod})\)
For any ring \(R\), the authors consider complete cotorsion pairs \((\mathcal{C},\mathcal{D})\) in the category \(\mathbf{C}(R-\mathrm{Mod})\) of complexes of left \(R\)-modules. If \(\mathcal{C}\) is closed under taking suspensions and \(\mathbf{K}(R-\mathrm{Mod})\) denotes the homotopy category, they prove that the embedding functors \(\mathbf{K}(\mathcal{C})\rightarrow \mathbf{K}(R-\mathrm{Mod})\) and \(\mathbf{K}(\mathcal{D})\rightarrow \mathbf{K}(R-\mathrm{Mod})\) have right and left adjoints, respectively. Examples of such cotorsion pairs and the corresponding induced adjoint situations are given in Section 4. Using results by \textit{M. Hovey} in [Math. Z. 241, No. 3, 553--592 (2002; Zbl 1016.55010)] that assure when a pair of classes of complexes of left \(R\)-modules gives rise to a model structure on \(\mathbf{C}(R-\mathrm{Mod})\), the authors finally describe a new model structure on \(\mathbf{C}(R-\mathrm{Mod})\) where the cofibrant objects are the projective ones.
scientific article; zbMATH DE number 6152186
scientific article