论文标题
Frobenius外部类别的稳定类别中的淤泥子类别的新表征
A new characterization of silting subcategories in the stable category of a Frobenius extriangulated category
论文作者
论文摘要
我们给出了Frobenius外侧类别稳定类别中的淤泥子类别的新表征，从而推广了Di等人的结果。 （J. Algebra 525（2019）42-63）关于三角形类别的淤积子类别的Auslander-Reiten类型对应。更具体地说，对于任何Frobenius外部策略类别$ \ MATHCAL {C} $，我们在稳定类别$ \ useverline {\ Mathcal {c}} $的淤塞子类别与某些协证的$ \ rathcal $ \ nathcal {c c} $ {c c。结果，给出了Frobenius精确类别稳定类别中的淤泥子类别的表征。该结果适用于Abelian类别的同型类别，具有足够的投影，具有足够的预测类别的派生类别，以及足够的投影以及稳定的Gorenstein Projective模块上的稳定类别。
We give a new characterization of silting subcategories in the stable category of a Frobenius extriangulated category, generalizing the result of Di et al. (J. Algebra 525 (2019) 42-63) about the Auslander-Reiten type correspondence for silting subcategories over triangulated categories. More specifically, for any Frobenius extriangulated category $\mathcal{C}$, we establish a bijective correspondence between silting subcategories of the stable category $\underline{\mathcal{C}}$ and certain covariantly finite subcategories of $\mathcal{C}$. As a consequence, a characterization of silting subcategories in the stable category of a Frobenius exact category is given. This result is applied to homotopy categories over abelian categories with enough projectives, derived categories over Grothendieck categories with enough projectives as well as to the stable category of Gorenstein projective modules over a ring $R$.
