本项目将以模型范畴的Quillen等价和Bousfield局部化、monoidal模型结构等为基本理论工具，将模型结构与三角范畴和Calabi-Yau代数的研究结合起来。在模型结构及同伦理论的框架下统一并推广复形同伦范畴的三角等价、三角矩阵代数上稳定范畴的粘合等已知结论，解决正合复形的同伦范畴的等价和粘合等需要新方法的问题，并得到环的导出等价和稳定等价在Quillen等价意义下的刻画。拟研究群环的模范畴以及微分分次模范畴的monoidal模型结构，并在一些同调不变量的计算中找到新的应用。拟用模型结构刻画Calabi-Yau代数和Calabi-Yau三角范畴，研究模型结构与Calabi-Yau性质的相容性。

In this project, we will take the Quillen equivalence and Bousfield localization of model categories, and monoidal model structures as the basic theoretical tools, to study triangulated categories and Calabi-Yau algebras. Established conclusions with respect to triangle-equivalence between homotopy categories of complexes and recollement of stable categories over triangular matrix algebras will be unified and generalized within the same framework of model structures and homotopy theories, so that problems on equivalences and recollements between homotopy categories of exact complexes can be solved, and derived equivalences and stable equivalences of rings can be described in the sense of Quillen equivalences. We will study monoidal model structures of categories of modules over group rings and differential graded modules, also for new applications in the computation of some homology invariants. Moreover, the model structures are used to characterize the Calabi-Yau algebras and the Calabi-Yau triangulated categories, to investigate when the model structure and the Calabi-Yau properties are compatible.