本项目主要研究微分分次范畴的模型结构、recollements和同伦范畴的紧性。将通过对微分分次范畴的余挠对性质的研究，试图在微分分次范畴中建立更多、更重要的模型结构；探求通过已知余挠对构造模型结构和新余挠对的一般方法；利用模型结构理论建立微分分次范畴的recollements。试图另辟蹊径研究微分分次同伦范畴的紧性和寻求一些与紧生成微分分次同伦范畴有关的recollements。考虑相对于微分分次范畴中余挠对(X,Y)的同伦子范畴K(X∩Y)的紧生成性及与之有关的伴随对，进而建立微分分次同伦（子）范畴间的各种recollements。本项目的研究对于丰富和发展微分分次范畴的模型结构理论、recollement理论和同伦范畴的紧生成理论具有重要的意义。

The main object of this project is to study model structures、recollements and the compact property of homotopy categories of differential graded categories. Through investigating properties of cotorsion pairs in differential graded categories, we will make an attempt to construct more and more important model structures in differential graded categories, explore a general method to construct model structures and new cotorsion pairs via known cotorsion pairs, and establish recollements of differential graded categories by using model structure theory. We will try to study the compact property of homotopy categories of differential graded categories and seek some recollements associated to compactly generated homotopy categories of differential graded categories by means of blazing a new trail. We will consider the compactly generated property of the homotopy subcategory K(X∩Y) and adjoint pairs related to K(X∩Y) with respect to a cotorsion pair (X,Y) in a differential graded category, and then create various recollements of homotopy (sub)categories of differential graded categories. The study of this project will play an important role in enriching and developing model structure theory、recollement theory and compactly generated theory of homotopy categories of differential graded categories.