本项目拟研究三角范畴中Gorenstein对象的稳定性，以及Gorenstein对象在模的同伦范畴和模的导出范畴中的具体表现形式，阐明与模范畴中Gorenstein对象之间的关系；通过比较和转换的方法，研究模范畴或Abel范畴中的余挠对与三角范畴中的挠对（t-结构）之间的联系，进而揭示Abel范畴与三角范畴之间的本质区别；以余挠对为工具，研究由Hovey三元组诱导的三角范畴的性质，借助于三角范畴的粘合，揭示它们之间的联系。. 这些研究将全面探索三角范畴中的相对同调性质，并以Hovey三元组为纽带，建立与模范畴或Abel范畴中相对同调性质间的紧密联系。这对进一步拓展三角范畴的应用范围具有重要意义。

The project will study the stability of Gorenstein objects in triangulated categories, as well as the concrete expression form of Gorenstein objects in the homotopy category of modules and the derived category of modules, to clarity the connection with Gorenstein objects in the category of modules. By using the method of comparison and transformation, we will study relationship between cotorsion pairs in the category of modules or an abelian category and torsion pairs (t-structures) in a triangulated category, to further reveal the essential properties in triangulated categories different from abelian categories. Moreover, taking cotorsion pairs as a tool, we will consider some triangulated categories induced by a Hovey triple, and reveal the connection between them by using recollements for triangulated categories.. These researchs will fully explore the relative homological properties for triangulated categories, and build close relationship for the relative homological properties between triangulated categories and the category of modules or abelian categories by Hovey triple. There will be of great significance to further expand the application scope of triangulated categories.