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

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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

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Abstract:

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
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