发表机构
Centro de Ciencias Matemáticas. Universidad Nacional Autónoma de México; Instituto de Matemática y Estadística “Prof. Ing. Rafael Laguardia”. Facultad de Ingeniería. Universidad de la República（墨西哥国立自治大学数学科学中心; 乌拉圭共和国大学工程学院拉富尔加里亚教授数学与统计研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过一类特殊的Frobenius对及其相对分解维数，构造了cotorsion对和模型结构，并应用于Gorenstein同调维数，得到相关的新结果。
AI 中文摘要
我们探索了一些从Frobenius对获得cotorsion对和模型范畴结构的方法。具体地，我们在阿贝尔范畴$\mathfrak{C}$中考虑一类Frobenius对$(\mathcal{X},\omega)$，对此存在一个非负整数$m$，使得$\mathcal{X}$在$\text{Ext}^1_{\mathfrak{C}}(-,\sim)$下的右正交补$\mathcal{X}^{\perp_1}$中的每个对象都有一个特殊的$\omega^\wedge_m$-预覆盖和一个特殊的$[\omega^\wedge_m]^{\perp_1}$-预包络，其中$\omega^\wedge_m$表示$\mathfrak{C}$中相对于$\omega$的分解维数至多为$m$的对象类。从这些Frobenius对获得的cotorsion对和模型结构将涉及类$\mathcal{X}$、$\omega$、$\mathcal{X}^\wedge_m$、$\omega^\wedge_m$及其正交补，用于描述其余纤维、纤维和普通对象。作为我们结果的应用，我们获得了与相对和绝对Gorenstein同调维数相关的若干cotorsion对和模型结构。
英文摘要
We explore some methods to obtain cotorsion pairs and model category structures from a Frobenius pair. Specifically, we consider a type of Frobenius pair $(\mathcal{X},ω)$ in an abelian category $\mathfrak{C}$ for which there exists a nonnegative integer $m$ such that every object in the right orthogonal complement $\mathcal{X}^{\perp_1}$ of $\mathcal{X}$ under $\text{Ext}^1_{\mathfrak{C}}(-,\sim)$ has a special $ω^\wedge_m$-precover and a special $[ω^\wedge_m]^{\perp_1}$-preenvelope, where $ω^\wedge_m$ denotes the class of objects in $\mathfrak{C}$ with resolution dimension relative to $ω$ at most $m$. The cotorsion pairs and model structures obtained from these Frobenius pairs will involve the classes $\mathcal{X}$, $ω$, $\mathcal{X}^\wedge_m$, $ω^\wedge_m$, and their orthogonal complements, in the description of its cofibrant, fibrant and trivial objects. As applications of our results, we obtain several cotorsion pairs and model structures related to relative and absolute Gorenstein homological dimensions.
Comments36 pages. No AI used. Comments are welcome
