本科生毕业设计（论文）详解.pdf

本科生毕业设计（论文） 题 目 拓扑范畴与代数范畴 姓名与学号 周晓晨 3033023015 指 导 教 师 黄兆镇 年级专业小班 理科班0301 所在学院和系 竺可桢学院 理科班 2007 年 6 月 10 日 Topological Categories and Algebraic Categories 拓扑范畴 与 代数范畴 Zhou Xiaochen 周晓晨 Zhejiang University 浙江大学 E-mail MSN : crision_cn@ June 5th, 2007 Abstract While the study of traditional category theory is focused on certain abstract categories and the functors between them, the study of concrete categories is aimed to find the properties of various structures on categories. A crucial viewpoint is that every faithful functor can be seen as a structure over the base category, so the study of structures changes into the study of faithful functors. Two of the important kinds of structures over categories are topological structures and algebraic structures, but such a saying is only an intuitive one. In my thesis I try to work out what is the essence of topological structures and algebraic structures. They both help greatly for us understanding the base categories, and some nice properties are reflected or preserved by these two kinds of functors. 摘要 传统的范畴学的研究集中在某些抽象范畴，和它们之间的函子，但是对具体范畴的研究却在 于探寻范畴之上的结构。一个关键的观点是，任何一个忠实函子都可以被认为是其上域范畴 上的一种结构，这样的话对范畴上结构的研究就变成了对忠实函子的研究。 范畴上两种最重要的结构是拓扑结构和代数结构，但是这仅仅是一种直观的说法。这篇论文 里我将指出拓扑结构和代数结构两个概念的精华所在。这两种函子都能帮助我们更好地理解 它们的上域范畴，而且它们能反映或保持许多优良的性质。 - 2 - Prerequisite Throughout the thesis, once the reader is confronted with an undefined term or