Let R be a ring, Q a small k-preadditive category, and let Q,RMod be the category of k-linear functors from Q to the left R-module category RMod. Given a cotorsion pair (𝒜,ℬ) in RMod, we construct four cotorsion pairs (Γ(𝒜), Γ(𝒜)⊥), (⊥Γ(ℬ), Γ(ℬ)), (Θ(𝒜), Θ(𝒜)⊥) and (⊥ξ(ℬ),ξ(ℬ)) in Q,RMod and investigate when these cotorsion pairs are hereditary and complete. Moreover, under few assumptions, we show that there exist a recollement of homotopy categories induced by these cotorsion pairs. Finally, some applications are given in the category of N-periodic chain complexes of R-modules.

中文翻译：

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自内射颤动上的函子类别模型

让R轴承，问一个小的ķ-preadditive 范畴，并让问,R模组成为的类别ķ- 线性函子来自问靠左R-模块类别R模组. 给定一个余量对(𝒜,ℬ)在R模组, 我们构造了四个 cotorsion 对(Γ(𝒜), Γ(𝒜)⊥),(⊥Γ(ℬ), Γ(ℬ)),(θ(𝒜), θ(𝒜)⊥)和(⊥ξ(ℬ),ξ(ℬ))在问,R模组并调查这些 cotorsion 对何时是遗传的和完整的。此外，在少数假设下，我们表明存在由这些 cotorsion 对诱导的同伦类别的回忆。最后，在类别中给出了一些应用程序ñ- 周期链配合物R-模块。