A Frobenius category within the monomorphism category
A Frobenius category within the monomorphism category
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单态范畴内的弗罗贝尼乌斯范畴
DOI：
10.1016/j.jalgebra.2020.01.002
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发表时间：
2020
影响因子：
0.9
通讯作者：
Lin Zhu
中科院分区：
文献类型：
--
作者：
Jian Feng;Peng Guo;Lin Zhu
给定一个自内射artin代数Λ，考虑一个左Λ-模在一个自生成内射左Λ-模中的所有嵌入的范畴Sinj（Λ）.证明了Sinj（Λ）是一个具有Auslander-Reiten序列的Frobenius范畴，使得范畴Λ-mod与Sinj（Λ）稳定等价，且Sinj（Λ）的不可分解内射对象是Λ-mod的两倍.
Given a selfinjective artin algebra Λ, we consider the category S inj (Λ) of all embeddings of a left Λ-module in a finitely generated injective left Λ-module. We show that S inj (Λ) is a Frobenius category with Auslander-Reiten sequences such that the categories Λ-mod and S inj (Λ) are stably equivalent and S inj (Λ) has twice as many indecomposable injective objects as Λ-mod.