发表机构
Faculty of Engineering Science, Kansai University（关西大学工学部）
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bi-Serre子范畴对连通加法幂等完备dg范畴上的精确dg结构进行内在分类，建立双射并给出完全格结构，同时提供Rump-Chen最大精确dg结构的另一构造。
AI 中文摘要
本文旨在将Enomoto关于精确结构的分类推广到dg层面。设$\mathscr{A}$为一个连通的加法幂等完备dg范畴。我们在$\mathsf{tr}(\mathscr{A})$中通过bi-Serre子范畴建立了$\mathscr{A}$上精确dg结构的一种内在的Enomoto型分类。我们的证明是基于3项复形的dg全化和dg对偶的直接dg论证，而非归结为最大精确dg结构及其子结构的分类。作为推论，我们在$\mathscr{A}$上的精确dg结构与$\mathsf{tr}(\mathscr{A})$中的bi-Serre子范畴之间建立了一个双射。此外，该双射是偏序集的同构，并在$\mathscr{A}$上的精确dg结构类上产生一个完全格结构。特别地，我们给出了Rump--Chen在$\mathscr{A}$上的最大精确dg结构的另一种构造。
英文摘要
The aim of this article is to leverage Enomoto's classification of exact structures to the dg level. Let $\mathscr{A}$ be a connective additive idempotent complete dg category. We establish an intrinsic Enomoto-type classification of exact dg structures on $\mathscr{A}$ in terms of bi-Serre subcategories in $\mathsf{tr}(\mathscr{A})$. Our proof is a direct dg argument based on dg totalizations of $3$-term complexes and dg duality, rather than a reduction to the greatest exact dg structure and the classification of its substructures. As a consequence, we establish a bijection between exact dg structures on $\mathscr{A}$ and bi-Serre subcategories in $\mathsf{tr}(\mathscr{A})$. Moreover, this bijection is an isomorphism of posets and yields a complete lattice structure on the class of exact dg structures on $\mathscr{A}$. In particular, we provide another construction of Rump--Chen's greatest exact dg structure on $\mathscr{A}$.
Comments25 pages
