稳定范畴与三角等价

Stable categories and triangulated equivalences

外三角范畴是三角范畴和正合范畴的推广,很多重要的结论都能统一在这个框架下.本文通过外三角范畴中的理想商实现了模型结构诱导的局部化商,即建立了这两种商范畴之间的三角等价.与此同时,也将此结果应用到Frobenius正合范畴、环R的同伦范畴和Gorenstein对象的稳定范畴.

Extriangulated categories are a generalization of triangular categories and exact categories,and many important conclusions can be unified under this framework.In this paper,the localized quotient induced by the model structure is realized by the ideal quotient in the extriangulated category,i.e.,the triangulated equivalence between the two quotient categories is established.At the same time,this result is also applied to the Frobenius exact category,the homotopy category of a ring R,and the stable category of Gorenstein objects.