CAJ | 학술논문

通过定义Gabriel单子来刻画模范畴的商范畴与局部化范畴，证明了Gabriel单子诱导的像和余像是等价的；其像为模范畴的局部化范畴，该局部化范畴等价于Gabriel单子确定的Kleisli范畴；其余像为模范畴的商范畴，该商范畴等价于Eilengerg-Moore范畴。
통과정의Gabriel단자래각화모범주적상범주여국부화범주，증명료Gabriel단자유도적상화여상시등개적；기상위모범주적국부화범주，해국부화범주등개우Gabriel단자학정적Kleisli범주；기여상위모범주적상범주，해상범주등개우Eilengerg-Moore범주。
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 equiv-alent to a Eilengerg-Moore category.