论文标题
$ q $形的派生类别 - 紧凑而完美的对象
The $Q$-shaped derived category of a ring -- compact and perfect objects
论文作者
论文摘要
在先前的工作中，我们构建了任何适当的$ q $ $ q $的$ q $形的派生类别。 $ a $ a $的$ q $形状类别，该类别由$ \ Mathcal {d} _ {q}（a）$表示，是普通派生类别的概括。在本文中，我们证明了$ a $的$ q $形派生类别是紧凑的三角形类别。我们还用$ \ Mathcal {d} _ {q}（a）$定义了完美对象，并证明这些对象构成了三角形的子类别，$ \ Mathcal {d}^\ Mathrm {perf} _ {q} _ {q} _ {q}（a）（a） $ q $形的派生类别中的紧凑型对象。子类别$ \ MATHCAL {D}^\ MATHRM {perf} _ {Q}（a）$和$ \ Mathcal {d} _ {q}（a）^\ mathrm {c} $ concine comcine concince concience cocine cosine gocide gocide gocide gocide gocide gocide gose
In a previous work we constructed the $Q$-shaped derived category of any ring $A$ for any suitably nice category $Q$. The $Q$-shaped derived category of $A$, which is denoted by $\mathcal{D}_{Q}(A)$, is a generalization of the ordinary derived category. In this paper we prove that the $Q$-shaped derived category of $A$ is a compactly generated triangulated category. We also define perfect objects in $\mathcal{D}_{Q}(A)$ and prove that these constitute a triangulated subcategory, $\mathcal{D}^\mathrm{perf}_{Q}(A)$, of the category $\mathcal{D}_{Q}(A)^\mathrm{c}$ of compact objects in the $Q$-shaped derived category. The subcategories $\mathcal{D}^\mathrm{perf}_{Q}(A)$ and $\mathcal{D}_{Q}(A)^\mathrm{c}$ coincide if and only if the former is thick.
