发表机构
Huaqiao University; Hunan Normal University; Gansu Center for Fundamental Research in Complex Systems Analysis and Control, Lanzhou Jiaotong University; Zhejiang Normal University（华侨大学; 湖南师范大学; 兰州交通大学复杂系统分析与控制甘肃省基础研究中心; 浙江师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对有限群G在满足|G|可逆的格罗滕迪克范畴𝒜上的作用，证明阿贝尔模型结构从𝒜到等变范畴𝒜^G的提升定理，构造关联导出函子的同伦方块并给出模范畴下的应用。
AI 中文摘要
设G为作用在具有足够投射对象的格罗滕迪克范畴𝒜上的有限群，且|G|在𝒜中可逆。我们证明了从𝒜到其等变范畴𝒜^G的阿贝尔模型结构的一般提升定理，并建立了对应同伦范畴之间的收缩下三角等价。我们还构造了一个交换方块，其水平函子为三角等价，垂直比较函子为收缩下三角等价，该方块将提升后的等变模型范畴上的导出函子与原同伦范畴导出函子的等变化联系起来。在模范畴情形下，我们利用PGF Hovey三元组说明上述结果，并将其应用于由弗罗贝尼乌斯双模及伴随型稳定等价诱导的同伦方块。
英文摘要
Let $G$ be a finite group acting on a Grothendieck category $\mathcal{A}$ with enough projectives, such that $|G|$ is invertible in $\mathcal{A}$. We prove a general lifting theorem for abelian model structures from $\mathcal{A}$ to its equivariant category $\mathcal{A}^G$, and establish a triangle equivalence up to retracts between the corresponding homotopy categories. We also construct a commutative square whose horizontal functors are triangle equivalences and whose vertical comparison functors are triangle equivalences up to retracts. This square relates derived functors on the lifted equivariant model categories to the equivariantizations of the derived functors on the original homotopy categories. In the module category setting, we illustrate the above results using the PGF Hovey triples, and apply them to homotopy squares induced by a Frobenius bimodule and by a stable equivalence of adjoint type.
Comments56 pages. In this version, we added a remark (Remark 2.17) to compare with Dalezios and Psaroudakis's work [Lifting recollements of abelian categories and model structures, J. Algebra 623 (2023), 395-446]
