三角范畴中Gorenstein对象的稳定性

Stability of Gorenstein objects in triangulated categories

设C是带有三角真类ξ的三角范畴.Asadollahi和Salarian引入并研究了ξ-Gorenstein投射和ξ-Gorenstein内射对象,并将Gorenstein同调代数发展到了三角范畴C中.本文继续研究三角范畴的Gorenstein同调性质.将对ξ-Gorenstein投射对象给出一些等价刻画,作为应用,得到了所有的ξ-Gorenstein投射对象构成的子范畴GP(ξ)有很好的稳定性.

Let C be a triangulated category with a proper duced and studied ξ-Gorenstein projective and ξ-Gorenstein class ξ of triangles. Asadollahi and Salarian intro- injeetive objects, and developed Gorenstein homo- logical algebra in C. In this paper, we further study Gorenstein homological properties for a triangulated category. We give some equivalent characterizations of ξ-Gorenstein projective objects, and show that the subeategory GP（ξ） of all ξ-Gorenstein projective objects has a nice stability, i.e., an iteration of the procedure used to define the ξ-Gorenstein projective objects yields exactly the ξ-Gorenstein projective objects.