DG范畴中性质(Ⅰ)的极限调整理论

Adjusting Limit Theorem of Property(Ⅰ) in DG Categories

三角结构是DG范畴的重要内容,其中,同伦极限理论是讨论三角结构的有力工具.一个DG模具有性质(P)指的是它具有被3个条件限制的特殊的filtration,但是其中极限过程这一条件可以被一个更为简洁的条件所取代,Keller证明了DG范畴中性质(P)的极限调整定理.文章首先证明了从具有性质(I)的DG模I出发能得到H A中的标准三角,并由此得DG范畴中性质(I)的极限调整定理及其证明.

Triangulate structure is an important content of DG categories.Homotopy limit theory is a powerful tool for discussing triangulate structure.A DG module with property（P） refers that it has a sequence of special filtration confined by three conditions.However one of the conditions,limiting process can be replaced by another more convenient and simpler one.The theorem of adjusting limits of property（P） in DG categories was firstly proved by B.Keller.Firstly the canonical triangulate structure in HA starting from module I of DG categories with property（P） was proved in this article.The adjusting limits of property（I） in DG categories as well as its proof of the theorem was obtained.