n角范畴的若干问题研究

发布时间：2018-04-03 22:50

本文选题：n角范畴　切入点：映射锥公理　出处：《华侨大学》2017年硕士论文

【摘要】：继三角范畴的发展以及高维同调代数的引入后,n角范畴自然而然地被提出.这种范畴在考虑加法范畴的某种高维丛倾斜子范畴时出现,并引起了众多数学工作者的关注.n角范畴是三角范畴的一种推广形式,经典三角范畴就是n角范畴中n(28)3的特殊情况.本文研究n角范畴高维映射锥公理的等价叙述、n角范畴的局部化理论、左n角范畴的稳定化,主要内容如下:第二章,利用同伦卡氏图等工具研究n角范畴中高维映射锥公理的等价叙述,证明了同伦卡氏图公理等价于高维映射锥,并由此证明了其他等价命题.第三章,介绍了n角范畴的相容乘法系,证明了n角范畴关于相容乘法系的局部化商范畴具有n角结构.第四章,证明了左n角范畴的稳定化范畴是n角范畴,并且左n角范畴的Grothendieck群与其稳定化范畴的Grothendieck群同构.
[Abstract]:Following the development of triangular category and the introduction of high dimensional homology algebra, the category of n angle is naturally proposed.This kind of category appears when considering some kind of high-dimensional bundle inclined subcategory of additive category, and it has aroused the attention of many mathematics workers that the category of .n angle is a kind of extension form of triangular category. The classical triangular category is the special case of nb283 in n-angle category.In this paper, we study the localization theory of n-angle category and the stabilization of left n-angle category. The main contents of this paper are as follows: chapter two,By means of homotopy Cartesian graphs and other tools, the equivalent description of the axioms of high-dimensional mapping cones in n-angle categories is studied, and it is proved that the axioms of homotopy Cardahs graphs are equivalent to high-dimensional mapping cones, and other equivalent propositions are proved.In chapter 3, we introduce the compatible multiplicative system of n-angle category, and prove that the localized-quotient category of n-angle category has n-angle structure.In chapter 4, we prove that the stabilized category of the left n-angle category is an n-angle category, and that the Grothendieck group of the left n-angle category is isomorphic to the Grothendieck group of its stabilized category.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O154.1

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