商范畴的幂等完备化

The Idempotent Completion of a Quotient Category

设M是加法范畴C上的理想,若商范畴C/M是幂等可提升的,令M=│a∈Mor(C)│a∈M│,本文证明商范畴C/M与对范畴C/M的幂等完备化范畴C/M是范畴等价的.

In this paper , the quotient category of an idempotent completed category C modulo M is proved to be equivalent to the idempotent completed category of the quotient category C/M, under the assumption that M is an ideal of the additive category C and the idempotent morphism in C can be lifted, where .M={a∈Mor（C）｜a∈M}.