论文标题
滑轮的基本介绍
A Very Elementary Introduction to Sheaves
论文作者
论文摘要
本文是对滑轮的非常不合格，松动且极为基本的介绍。这是为了获得有关滑轮的直觉，它们的外观以及它们的工作方式的指南，以便在阅读本文后，有人可以在教科书中看到非常抽象的定义和示例，至少对正在发生的事情有所了解。这些材料的大部分都是受到迈克尔·罗宾逊（Michael Robinson）博士的启发和建立的，罗伯特·格里斯特（Robert Ghrist）博士和雅各布·汉森（Jakob Hansen）博士以及贾斯汀·库里（Justin Curry）博士的博士学位论文是，他们是那里唯一的应用造纸条理论家，他们在研究过程中以合理的方式来解释冰淇淋的工作很棒。本文的其余部分是由教科书中发现的数学定义填充，这些定义我已经从两行延伸到多页，以及一些我想到自己的滑轮的类比。本文仅假定基本线性代数，基本群体理论和拓扑基础知识的知识。如果您不明白的设置中有任何内容，那可能是快速的Wikipedia搜索。我希望本文提供洞察力，直觉和有用的例子，说明为什么滑轮是数学和科学中如此强大的工具。
This paper is a very non-rigorous, loose, and extremely basic introduction to sheaves. This is meant to be a a guide to gaining intuition about sheaves, what they look like, and how they work, so that after reading this paper, someone can jump into the extremely abstract definitions and examples seen in textbooks with at least some idea of what is going on. Most of this material is inspired and built from the work of Dr. Michael Robinson, and that of Dr. Robert Ghrist and Dr. Jakob Hansen, as well as Dr. Justin Curry's PhD thesis, who are some of the only applied sheaf theorists out there and they do an amazing job of explaining sheaves in a concrete way through their research. The rest of this paper is populated by mathematical definitions found in textbooks that I have stretched from two lines into multiple pages, as well as some analogies for thinking of sheaves I have thought of myself. This paper only assumes knowledge of basic linear algebra, basic group theory, and the very fundamentals of topology. If there is anything in the setup that you do not understand it is probably a quick Wikipedia search away. I hope this paper provides insight, intuition, and helpful examples of why sheaves are such powerful tools in both math and science.
