三角范畴局部化的若干注记

发布时间：2017-12-27 05:25

本文关键词：三角范畴局部化的若干注记　出处：《安徽大学》2015年硕士论文　论文类型：学位论文

更多相关文章： 三角范畴 三角函子 局部化 乘法系

【摘要】：近三十年来,三角范畴在数学的各分支发挥着重要作用,如代数表示论,代数几何,拓扑学等.局部化理论是研究三角范畴的重要工具.设S为三角范畴K的相容乘法系,S-1K为K相对S的局部化范畴.另一方面,记K的子范畴存在好三角使得f∈S}.众所周知,S为饱和相容乘法系当且仅当ψ(S)为一个厚三角子范畴。但一般来说,ψ(S)不一定是K的三角子范畴。本文主要研究相容乘法系S的内蕴性质与局部化函子以及子范畴ψ(S)之间的关系.文章主要安排如下：第一章,我们回顾了三角范畴及其局部化理论的研究背景、主要研究方法与发展历史,以及论文的主要结构.第二章,我们系统回顾了本文所用到的一些基本概念与一些熟知的主要结果,主要包括三角范畴、三角函子、乘法系、一般范畴的局部化、三角范畴的局部化、厚子范畴和饱和相容乘法系等.第三章,主要介绍了三角范畴局部化中三角子范畴的厚闭包以及乘法系的饱和闭包,并讨论了由三角子范畴确定的相容乘法系的饱和闭包与其厚闭包确定的乘法系之间的关系.最后一章,我们首先回顾了一个熟知的结果,即饱和相容乘法系和厚子范畴一一对应,并给出了一个新的证明.进一步,我们给出弱饱和乘法系的定义,证明了由三角子范畴确定的乘法系是强乘法系以及由弱饱和相容乘法系确定的全子范畴是一个三角子范畴.
[Abstract]:In the past thirty years, delta category plays an important role in various branches of mathematics, such as algebraic representation theory, algebraic geometry and topology. The localization theory is an important tool to study the triangulated category. Let S be multiplicative system of Triangulated Categories K, S-1K for the localization of category relative to S K. On the other hand, K the sub category of existing triangle makes f in S}. S is saturated multiplicative as everyone knows, when and only when the PSI (S) as a thick three slot category. But in general, psi (S) is not necessarily a subcategory of K triangle. The intrinsic nature and localization functor and sub category properties this paper mainly studies the multiplicative system of S (S). The relationship between the article mainly as follows: the first chapter, we review the development and research background, main research methods and theory of localization triangulated category of history, and the main structure of the paper. The second chapter, we systematically reviewed some of the basic concepts used in this paper and some well-known results, including category, triangle, triangle functor, multiplication of the general category of localization, the localization of Triangulated Categories, thick subcategories and saturated multiplicative system. The third chapter mainly introduces the saturated closure triangular sub category in the localization of Triangulated Categories and thick closure multiplication system, and discusses the relationship between the multiplicative system determined by the triangular sub category of multiplicative system saturated with thickness determined by the closure of the closure last. Chapter, we first review a well-known results, namely saturated multiplicative system and thick subcategory of correspondence, and gives a new proof. Further, we give the definition of weak saturated multiplication system, that is determined by the triangular sub category by law by law and is strong by full subcategory weak saturated multiplicative system is determined by a triangular sub category.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O154.1

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