发表机构
School of Mathematics and Statistics, Hunan Normal University（湖南师范大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于二分图的组合判据，用于广义Reedy范畴标准模的投射性，恢复并推广了Dold-Kan型等价，并应用于有限域上仿射等空间的表示。
AI 中文摘要
我们引入了一个组合判据，用于广义Reedy范畴上标准模的投射性，该判据以有限二分图的形式表述，其规范化权重决定规范化幂等元，从而决定标准模的投射分解。我们将此框架应用于恢复若干经典规范化构造和Dold-Kan型等价，并为有限域上有限维仿射空间、半线性空间和半仿射空间的范畴获得新的Dold-Kan型等价。这些等价还给出了相应无限变换幺半群的均匀连续表示的显式描述。结合我们先前关于标准模之间Hom空间的工作，这些结果提供了一种主要基于图论和线性代数的组合机制，用于建立广义Reedy范畴的Dold-Kan型等价。
英文摘要
We introduce a combinatorial criterion for the projectivity of standard modules over generalized Reedy categories, formulated in terms of a finite bipartite graph whose normalized weightings determine normalization idempotents and hence projective splittings of standard modules. We apply this framework to recover several classical normalization constructions and Dold--Kan--type equivalences, and to obtain new Dold--Kan--type equivalences for categories of finite-dimensional affine, semilinear, and semiaffine spaces over a finite field. These equivalences also yield explicit descriptions of uniformly continuous representations of the corresponding infinite transformation monoids. Together with our previous work on Hom-spaces between standard modules, the results provide a combinatorial machinery, based mainly on graph theory and linear algebra, for establishing Dold--Kan--type equivalences for generalized Reedy categories.
