给定一个有足够多同调对象的正合范畴，我们将构造无界复形的同调分解；建立同伦范畴的稳定t-结构并讨论其导出范畴。考察在某些正合范畴中，特殊复形由正合到可裂的事实，对这一现象给出若干一般性的判定条件；并利用这些结果研究同调猜想。对于同伦范畴的一个稳定t-结构，研究其何时决定一个具有足够多同调对象的正合结构。在此基础上尝试对同伦范畴中的recollements进行分类并对Roos猜想展开讨论。

We will construct homological resolutions of unbounded complexes over a giving exact category with enough homological objects; we will build stable t-structures in its homotopy category and study the corresponding derived category. In view of the facts that exactness implies splitting for special complexes in some exact categories, we will give several criterions for this phenomenon and apply them to homological conjectures. Suppose that there exists a stable t-structure in a homotopy category. Then we will discuss whether it determines an exact structure with enough homological objects. Based on this work, we will try to classify recollements in homotopy categories, and consider Roos' conjecture.