发表机构
Hunan Normal University（湖南师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究广义Reedy范畴标准模间同态，提供统一可计算框架简化构造，建立Dold - Kan对应统一扩展，为代数拓扑和表示理论多个结果提供概念基础。
AI 中文摘要
我们通过对标准模之间同态空间的系统研究，开发了一种用于广义Reedy范畴的表示理论方法。对于这类范畴中的一大类，我们提供了一个统一的、可计算的框架，通过关联矩阵和态射纤维将抽象的同调构造简化为初等线性代数和谱图理论。作为主要应用，我们为源于有根树的范畴建立了Dold - Kan对应的统一扩展，涵盖有限链、有限集和部分单射以及有限蜘蛛的范畴。关键的是，该机制统一并为代数拓扑和表示理论中的几个经典但看似不同的结果提供了一个独特的概念基础，包括向量空间的Kuhn分解定理和Mackey函子的Thévenaz - Webb半单性定理。
英文摘要
We develop a representation-theoretic approach to generalized Reedy categories through a systematic study of homomorphism spaces between standard modules. For a broad class of these categories, we provide a uniform, computable framework that reduces abstract homological constructions to elementary linear algebra and spectral graph theory via incidence matrices and morphism fibers. As a primary application, we establish a uniform extension of the Dold--Kan correspondence for categories arising from rooted trees, encompassing the categories of finite chains, finite sets and partial injections, and finite spiders. Crucially, this machinery unifies and provides a singular conceptual basis for several classic, seemingly disparate results across algebraic topology and representation theory, including Kuhn's decomposition theorem for vector spaces and the Thévenaz--Webb semisimplicity theorem for Mackey functors.
CommentsTitle changed, some typographic issues corrected, and referenced updated
