本项目主要研究同伦范畴的recollement、(余)t-结构和复形的同调维数理论。我们将从Abel复形范畴中各种预覆盖预包络的存在性和余挠对的完备性出发，建立同伦范畴间的三角伴随函子和(余)t-结构，探求三角伴随和(余)t-结构存在的一般条件；利用局部化余局部化序列和模型结构理论，构造同伦范畴的recollement和导出等价，并考查Abel范畴和同伦范畴中的余挠对、模型结构、recollement和(余)t-结构之间的相互关系；从满足一定条件的余挠对和诱导的模型结构出发，开展无界复形同调维数一般理论的研究；利用适当的模型结构和导出等价给出各种维数的同调刻画及不同维数的区别和联系；通过余挠对的不同选取得到建立和计算导出函子同调群的新途径，进而研究复形的更多同调性质。本研究将丰富和发展同伦范畴的recollement、(余)t-结构和复形的同调维数理论，以推动代数学及其它学科的进一步发展。

The main object of project is to study the recollement,(co)t-structure of homotopy categories and homological dimension theory of complexes. We will study the existence of precover and preenvelope of objects in the category of Abel complexes and study completeness of cotorsion pairs,to establish triangulated adjoint functors and (co)t-structures of homotopy categories, to find general conditions of existence of triangulated adjoint and (co)t-structure. We will establish recollement and derived equivalences of homotopy categories by using of localising and colocalising sequences and model sreucture theories, and consider the relationships between cotorsion pair, model structure, recollement and (co)t-structure in Abel categories and homotopy categories. Base on the suitable cotorsion pairs and the induced model structures, we will develope the general theory of homological dimensions of the infinite complex. In view of model structures and derived equivalences, we will give some homological characterizations of these dimensions and consider differences and relations between different dimensions. The new ways of establishing and computing derived functor cohomology group will follow from our results by choosing of cotorsion pairs. Further, we will study more homological properties of complexes. The study of this project will enrich and develop the recollement, (co)t-structure of homotopy categories and homological dimension theory of complexes, and further promote the development of algebra and other subjects.