论文标题
简要说明Posets上的捆结构
A Brief Note for Sheaf Structures on Posets
论文作者
论文摘要
该注释是在台湾师范大学的数学系，2020年跌倒的研究生代数几何学研讨会的一部分。它的目的是引入一个带有Alexandrov拓扑的POSET上定义的绳索示例，称为细胞或骨。细胞捆是从Poset类别到特定代数结构类别（例如组类别）的函数。严格来说，即使将Poset配备了Alexandrov拓扑，这只是Alexandrov拓扑空间上的前账的定义。通过检查详细信息，细胞或骨实际上是拓扑空间上的束带。这是通过KAN扩展中的捆绑理论中众所周知的事实，而它要求熟悉类别理论的读者。在本说明中，我们遵循一种基本方法来描述代数几何形状中相关的细胞或骨之间的连接，其中仅需要基本的交换代数和点集拓扑作为背景知识。
This note is a part of the lecture notes of a graduate student algebraic geometry seminar held at the department of mathematics in National Taiwan Normal University, 2020 Falls. It aims to introduce an example of sheaves defined on posets equipped with the Alexandrov topology, called the cellular sheaves. A cellular sheaf is a functor from the category of a poset to the category of specific algebraic structures (e.g. the category of groups). Strictly speaking, even equipping the poset with the Alexandrov topology, it is just the definition of a pre-sheaf on the Alexandrov topological space. By checking details, cellular sheaves are actually sheaves on topological spaces. This is a well-known fact in sheaf theory via the Kan extension, while it requires readers who are familiar with the category theory. In this note, we follow an elementary approach to describe the connection between cellular sheaves and sheaves concerned in algebraic geometry, where only basic commutative algebra and point-set topology are required as the background knowledge.
