论文标题
在$ n $ cluster倾斜子类别的单态类别上
On the Monomorphism Category of $n$-Cluster Tilting Subcategories
论文作者
论文摘要
令$ \ mathcal {m} $为$ n $ -cluster倾斜子类别的$ {\ rm mod} \ mbox { - }λ$，其中$λ$是Artin代数。令$ \ mathcal {s}（\ Mathcal {M}）$表示$ \ Mathcal {s}（λ）$的完整子类别，$λ$的子模型类别，由所有单态$ \ Mathcal {m} $组成。我们从$ \ Mathcal {s}（\ Mathcal {m}）$构造两个函数，到$ {\ rm mod} \ mbox { - } \ usewissline {\ Mathcal {m Mathcal {m}} $，在$ nath $ $ n $ nath $ and $ contector（coherent）contriant contriant contriant functors的类别中我们表明这些函子是充分，密集和客观的。因此，它们从$ \ Mathcal {m} $ modulo的子模块类别的商类别中引起等价。此外，它们是由$ {\ rm mod} \ mbox { - } \ Uneseline {\ Mathcal {M}} $的稳定类别上的Syzygy Fuctor关联的。这些函子可以被认为是Ringel和Zhang [rz]在$λ= k [x]/{\ langle x^n \ rangle} $的情况下研究的两个函子的更高版本，后来由Eiríksson[e]概括为自给自足的Armentive Armentive Artin Algebras。将提供几种申请。
Let $\mathcal{M}$ be an $n$-cluster tilting subcategory of ${\rm mod}\mbox{-}Λ$, where $Λ$ is an artin algebra. Let $\mathcal{S}(\mathcal{M})$ denotes the full subcategory of $\mathcal{S}(Λ)$, the submodule category of $Λ$, consisting of all monomorphisms in $\mathcal{M}$. We construct two functors from $\mathcal{S}(\mathcal{M})$ to ${\rm mod}\mbox{-}\underline{\mathcal{M}}$, the category of finitely presented (coherent) additive contravariant functors on the stable category of $\mathcal{M}$. We show that these functors are full, dense and objective. So they induce equivalences from the quotient categories of the submodule category of $\mathcal{M}$ modulo their respective kernels. Moreover, they are related by a syzygy functor on the stable category of ${\rm mod}\mbox{-}\underline{\mathcal{M}}$. These functors can be considered as a higher version of the two functors studied by Ringel and Zhang [RZ] in the case $Λ=k[x]/{\langle x^n \rangle}$ and generalized later by Eiríksson [E] to self-injective artin algebras. Several applications will be provided.
