三角范畴的Recollement与Abel化

Recollement and Abelian of Triangulated Category

首先给出了加法范畴的Abel化与幂等完备化的关系,证明了加法范畴的幂等完备化范畴是其Abel化范畴的投射子范畴;在此基础上,证明了三角范畴recollement的Abel化是Abel范畴的右recollement。

The relationship between Abelian and idempotent completion of additive categories was presented in this paper. It proves that the idempotent completion of an additive category is the subcategory of its Abelian category, which consists of all the projectives. Then we prove that the Abelian of a recollement of triangulated categories is a right recollement of Abelian categories.