函子范畴与幂等完备化构造的相容性

Compatibility of Functor Category and Idempotent Complete Construction

讨论函子范畴和范畴的幂等完备化构造的相容性,证明小范畴■到任意范畴■的函子范畴■的幂等完备化范畴等价于■到幂等完备化范畴■的函子范畴■.进一步得到函子范畴■是幂等完备的,当且仅当■是幂等完备的.

Investigate the compatibility of functor categories and idempotent completion construction.It proves that the idempotent complete category of the functor category■from small category■to any category■is equivalent to the functor category■from■to idempotent complete category■Then,the functor category■is idempotent complete if and only if■is idempotent complete.