论文标题
灯塔类别中的平面模型结构和Gorenstein对象
Flat model structures and Gorenstein objects in functor categories
论文作者
论文摘要
我们在类别上构建平面模型结构$ _ {\ Mathcal {q}，r} {\ MathSf {mathsf {mod}} $来自一个小的preadditive类别$ \ MATHCAL {Q} $的添加剂函数，将某些条件满足模块类别$ _ whros $ _ whros $ _ whros $}类别是Holm和Jorgensen引入的$ \ MATHCAL {Q} $形状的类别。此外，我们证明，对于一个任意的关联环$ r $，一个$ _ {\ Mathcal {q}，r} {\ mathsf {modsf {mod}} $的对象是Gorenstein Projective（gorenstein，Gorenstein Inpove。 $ \ MATHCAL {Q} $，因此改善了Dell'ambrogio，Stevenson和šťov\'ıček的结果。
We construct a flat model structure on the category $_{\mathcal{Q},R}{\mathsf{Mod}}$ of additive functors from a small preadditive category $\mathcal{Q}$ satisfying certain conditions to the module category $_{R}{\mathsf{Mod}}$ over an associative ring $R$, whose homotopy category is the $\mathcal{Q}$-shaped derived category introduced by Holm and Jorgensen. Moreover, we prove that for an arbitrary associative ring $R$, an object in $_{\mathcal{Q},R}{\mathsf{Mod}}$ is Gorenstein projective (resp., Gorenstein injective, Gorenstein flat, projective coresolving Gorenstein flat) if and only if so is its value on each object of $\mathcal{Q}$, and hence improve a result by Dell'Ambrogio, Stevenson and Šťov\'ıček.
