双单子的Smash积

吉林大学学报(理学版)

双单子的Smash积

郭双建¹, 张晓辉²

1. 贵州财经大学数学与统计学院, 贵阳 550025; 2. 东南大学数学系, 南京 210096

收稿日期:2015-01-14 出版日期:2015-09-26 发布日期:2015-09-29
通讯作者: 郭双建 E-mail:shuangjguo@gmail.com

Smash Product of Bimonads

GUO Shuangjian¹, ZHANG Xiaohui²

1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China;2. Department of Mathematics, Southeast University, Nanjing 210096, China

Received:2015-01-14 Online:2015-09-26 Published:2015-09-29
Contact: GUO Shuangjian E-mail:shuangjguo@gmail.com

摘要/Abstract

摘要：

考虑双单子Smash积的表示范畴. 设F和G是给定的双单子, 利用2范畴方法讨论其Smash积GF上的张量结构, 证明了GF的双单子结构与其表示范畴上的张量结构是等价的, 并给出了其表示范畴做成张量范畴的一系列充要条件.

关键词: 双单子, Smash积, 张量范畴, 2范畴

Abstract:

The aim of this paper is to define and study the Smash product of two bimonads. Assume that F and G are bimonads, GF denotes their Smash product, the monoidal structure of GF was discussed via the theory of 2category. We showed that the bimonad structure of GF is equivalent to the monoidal structure of GFmodules. Finally, we gave necessary and sufficient conditions for the category of GFmodules to be a monoidal category.

Key words: bimonad, Smash product, monoidal category, 2category

中图分类号:

O154.1

郭双建, 张晓辉. 双单子的Smash积[J]. 吉林大学学报(理学版), 2015, 53(05): 914-920.

GUO Shuangjian, ZHANG Xiaohui. Smash Product of Bimonads[J]. Journal of Jilin University Science Edition, 2015, 53(05): 914-920.