## Abstract

In [8] Salce introduced the notion of a cotorsion pair (A, B) in the category of abelian groups. But his definitions and basic results carry over to more general abelian categories and have proved useful in a variety of settings. In this article we will consider complete cotorsion pairs (C,D) in the category C(R-Mod) of complexes of left R-modules over some ring R. If (C ,D) is such a pair, and if C is closed under taking suspensions, we will show when we regard K(C) and K(D) as subcategories of the homotopy category K(RMod), then the embedding functors K(C) → K(R-Mod) and K(D) → K(R-Mod) have left and right adjoints, respectively. In finding examples of such pairs, we will describe a procedure for using Hoveys results in [5] to find a new model structure on C(R-Mod).

Original language | English |
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Pages (from-to) | 1787-1802 |

Number of pages | 16 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 42 |

Issue number | 6 |

DOIs | |

State | Published - 2012 |

## Keywords

- Adjoint functors
- Complexes
- Cotorsion pairs