Abstract
Let R be a ring with 1 and M a right R-module. In this article, we will see that the functor F = M ⊗ R – gives rise to a complete hereditary cotorsion pair where the left class consists of the F-acyclic objects. This cotorsion pair induces a Quillen model structure on Ch(R) which recovers the derived functors . An F-acyclic resolution is as good as a cofibrant replacement in this model structure. So in short, we formalize the fact that can be computed using F-acyclic resolutions.
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