您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (4): 30-34.doi: 10.6040/j.issn.1671-9352.0.2015.187

• • 上一篇    下一篇

Monoidal范畴的两种构造

冯清1,黄菊2*   

  1. 1.福建师范大学福清分校电子与信息工程学院, 福建 福清 350300;2.福建师范大学数学与计算机科学学院, 福建 福州 350117
  • 收稿日期:2015-04-23 出版日期:2016-04-20 发布日期:2016-04-08
  • 通讯作者: 黄菊(1990— ), 女, 博士, 研究方向为代数表示论. E-mail:Hj20140429@163.com E-mail:fqingmath@163.com
  • 作者简介:冯清(1982— ), 女, 讲师, 研究方向为代数表示论. E-mail:fqingmath@163.com
  • 基金资助:
    国家自然科学基金资助项目(11471269,11071040);福建省自然科学基金资助项目(2010J01001)

Two constructions of monoidal categories

FENG Qing1, HUANG Ju2*   

  1. 1. Department of Electronic and Information Engineering, Fuqing Branch of Fujian Normal University, Fuqing 350300, Fujian, China;
    2. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350117, Fujian, China
  • Received:2015-04-23 Online:2016-04-20 Published:2016-04-08

摘要: 通过范畴的扩张构造两类monoidal范畴。给定一个monoidal范畴,构造了一个回路范畴并证明其仍然为monoidal范畴。给定一个加法monoidal范畴及一个加法严格monoidal函子,证明可以构造一个仍然为monoidal范畴的平凡扩张范畴。

关键词: 平凡扩张, 回路范畴, Monoidal范畴

Abstract: Two monoidal categories by the extensions of category are constructed, and it is proved that a loop category of a given monoidal category is a monoidal category. For an additive monoidal category and an additive strict monoidal functor, it is proved that its trivial extension is a monoidal category.

Key words: loop category, monoidal category, trivial extension

中图分类号: 

  • O154.1
[1] LANE S M. Categories for the working mathematician[M] // Graduate Texts in Mathematics 5: 2nd edition. New York: Springer-verlag, 1998.
[2] HUANG Hualin, OYSYAEYEN F V, YANG Yuping, et al. The Green rings of pointed tensor categories of finite type[J]. Journal of Pure and Applied Algebra, 2014, 218(2):333-342.
[3] HUANG Hualin, LIU Guoxiang, YE Yu. Quivers, quasi-quantum groups and finite tensor categories[J]. Comm in Math Physics, 2011, 3(303):595-612.
[4] THOMASON R W. Symmetric monoidal categories model all connective spectra[J]. Theory and Applications of Categories, 1995, 1(5):78-118.
[5] BASS H. Algebraic K-theory[M]. New York: Benjamin, 1968.
[6] FOSSUM R M, GRIFFITH P A, REITEN I. Trivial extensions of abelian categories[M]. New York: Springer-Verlag, 1975.
[1] 郭双建,李怡铮. 拟Hopf代数上BHQ何时是预辫子monoidal范畴[J]. 山东大学学报(理学版), 2017, 52(12): 10-15.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!