AI 中文总结
本研究基于PGF对象建立统一方法构造图表范畴的平坦模型结构，将其应用于Q形导出范畴得到涵盖复形经典构造的统一框架，并明确了模型的余纤维对象。
AI 中文摘要
我们开发了一种基于投影消解Gorenstein平坦（PGF）对象的统一方法，用于在图表范畴上构造平坦模型结构。具体而言，我们证明这类范畴中的PGF对象完全由其逐点分量决定，这使我们能建立遗传阿贝尔模型结构，其平凡余纤维对象恰好是平坦对象。作为应用，我们重新得到Q形导出范畴上的平坦模型结构，从而提供了一个涵盖复形经典构造的统一框架，还明确描述了这些模型中的余纤维对象。
英文摘要
We develop a unified approach, based on projectively coresolved Gorenstein flat (PGF) objects, for constructing flat model structures on diagram categories. Specifically, we show that PGF objects in such categories are fully determined by their objectwise components, which in turn enables us to establish hereditary abelian model structures whose trivial cofibrant objects are precisely the flat objects. As an application, we reobtain flat model structures on $Q$-shaped derived categories, thereby providing a common framework that subsumes classical constructions for chain complexes. Moreover, we obtain an explicit description of the cofibrant objects in these models.
