[1]林妹珠,蔡菊香,陈清华.半群分次范畴的Smash积[J].华侨大学学报(自然科学版),2008,29(3):455-458.[doi:10.11830/ISSN.1000-5013.2008.03.0455]
　LIN Mei-zhu,CAI Ju-xiang,CHEN Qing-hua.Smash Product of Semigroup-Graded Category[J].Journal of Huaqiao University(Natural Science),2008,29(3):455-458.[doi:10.11830/ISSN.1000-5013.2008.03.0455]
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半群分次范畴的Smash积()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第29卷
期数:
2008年第3期
页码:
455-458
栏目:
出版日期:
2008-07-20

文章信息/Info

Title:
Smash Product of Semigroup-Graded Category
文章编号:
1000-5013(2008)03-0455-04
作者:
林妹珠; 蔡菊香; 陈清华
福建农林大学计算机与信息学院; 福建师范大学数学与计算机科学学院; 福建师范大学数学与计算机科学学院 福建福州350002; 福建福州350007
Author(s):
LIN Mei-zhu1;  CAI Ju-xiang2;  CHEN Qing-hua2
1.College of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, China; 2.School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
关键词:
自由半群作用范畴;  商范畴;  半群分次范畴;  Smash积
Keywords:
free semigroup action category;  quotient category;  semigroup-graded category;  Smash product
分类号:
O152.7
DOI:
10.11830/ISSN.1000-5013.2008.03.0455
文献标志码:
A
摘要:
设S为有单位元1的可消半群,引入半群S-分次范畴的Smash积的概念,分别证明半群S-分次范畴C的Smash积C#S的商范畴(C#S)/S与范畴C同构,以及自由半群S-范畴B的商范畴B/S的Smash积范畴(B/S)#S与范畴B同构.从而说明半群分次范畴的Smash积与自由半群作用范畴的商在半群分次范畴和自由半群作用范畴之间是互逆的结构.
Abstract:
For Smash product of semigroup-graded category,we prove that the quotient category(C#S)/S of Smash product C#S of semigroup S graded category C is isomorphic to category C,and the Smash product category(B/S)#S of the quotient category B/S of free semigroup S category B is isomorphic to category B when S is a cancellative semigroup with identity 1.It is shown that the semigroup-graded categorical Smash product and the semigroup categorical quotient are inverse structions between semigroup-graded categories and free semigroup action categories.

参考文献/References:

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备注/Memo

备注/Memo:
国家自然科学基金资助项目(10371101); 福建省自然科学基金资助项目(Z0511022); 福建省教育厅科研基金资助项目(JA05206,JB04251); 福建农林大学青年教师科研基金资助项目(021747)
更新日期/Last Update: 2014-03-23