关键词: 商范畴, 局部化, Gabriel单子

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