本文選題：n角范疇　切入點(diǎn)：映射錐公理　出處：《華僑大學(xué)》2017年碩士論文

【摘要】：繼三角范疇的發(fā)展以及高維同調(diào)代數(shù)的引入后,n角范疇自然而然地被提出.這種范疇在考慮加法范疇的某種高維叢傾斜子范疇時(shí)出現(xiàn),并引起了眾多數(shù)學(xué)工作者的關(guān)注.n角范疇是三角范疇的一種推廣形式,經(jīng)典三角范疇就是n角范疇中n(28)3的特殊情況.本文研究n角范疇高維映射錐公理的等價(jià)敘述、n角范疇的局部化理論、左n角范疇的穩(wěn)定化,主要內(nèi)容如下:第二章,利用同倫卡氏圖等工具研究n角范疇中高維映射錐公理的等價(jià)敘述,證明了同倫卡氏圖公理等價(jià)于高維映射錐,并由此證明了其他等價(jià)命題.第三章,介紹了n角范疇的相容乘法系,證明了n角范疇關(guān)于相容乘法系的局部化商范疇具有n角結(jié)構(gòu).第四章,證明了左n角范疇的穩(wěn)定化范疇是n角范疇,并且左n角范疇的Grothendieck群與其穩(wěn)定化范疇的Grothendieck群同構(gòu).
[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.
【學(xué)位授予單位】：華僑大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O154.1

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相關(guān)期刊論文 前2條

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本文編號(hào)：1707275