JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (2): 24-28.doi: 10.6040/j.issn.1671-9352.0.2013.173

• Articles • Previous Articles     Next Articles

The Gabriel monad and the localization of R-module category

LIU Yang1, WANG Zheng-ping2, XU Qing-bing2   

  1. 1. Department of Mathematics Chuzhou College, Chuzhou 239000, Anhui, China;
    2. Chuzhou Vocational and Technical College, Chuzhou 239000, Anhui, China
  • Received:2013-04-10 Online:2014-02-20 Published:2014-06-04


A Gabriel monad is defined as the idempotent monad to characterize the quotient category and localization of R-module category, and prove that the Gabriel monad induces an equivalence between its image and coimage, its image is the localization category which is equivalent to a Kleisli category; its coimage is the quotient category which is equivalent to a Eilengerg-Moore category.

Key words: quotient category, localization, Gabriel monad

CLC Number: 

  • O154.1
[1] REN Chun-nian, GAO Jian. A theory research and experiment scheme on enable-control Anderson localization and delocalization based on quantum walk [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 61-66.
[2] ZHAO Feng, XU Xiu. An improved DV-hop algorithm based on iterative computation and two communication ranges for sensor network localization [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(07): 31-37.
[3] On the quotient category and localization of an R-module Category. On the quotient category and localization of an R-module Category [J]. J4, 2013, 48(4): 46-50.
[4] L Jia-liang1,2,3, WANG Ying-long1,3, CUI Huan-qing1, WEI Nuo2,3, GUO Qiang2,3. Study on the node localization schemes of three dimensional wireless sensor networks based on particle swarm optimization [J]. J4, 2013, 48(05): 78-82.
[5] CUI Huan-qing1,2, WANG Ying-long1*, L Jia-liang1,2, WEI Nuo1. Distributed node localization based on the stochastic particle swarm optimization [J]. J4, 2012, 47(9): 51-55.
[6] CAO Hai-song, WU Jun-liang. On localization of eigenvalues in elliptic region [J]. J4, 2012, 47(10): 49-53.
[7] ZHOU Shu-wang1,2,3, WANG Ying-long1,3, GUO Qiang1,2, WEI Nuo1,2, GUO Wen-juan1,3. A new method for localization based on network  coverage and intelligent search [J]. J4, 2010, 45(11): 27-31.
Full text



No Suggested Reading articles found!