Recollement导出的共变与反变有限子范畴

The Covariantly Finite and Contravariantly Finite Subcategories Induced by Recollements

证明了若3个三角范畴允许有1个recollement,则recollement两端三角范畴上的共变有限子范畴可以诱导出中间三角范畴上的1个共变有限子范畴;对偶地,recollement两端三角范畴上的反变有限子范畴也可诱导出中间三角范畴上的1个反变有限子范畴.进一步地,将其应用到具体范畴,得到几类导出范畴的共变有限子范畴及反变有限子范畴.

In this paper,we prove that if there is a recollement of triangulated categories,then the covariantly finite subcategories on both ends can induce a covariantly finite subcategory on the middle one.Dually,the contravariantly finite subcategories on both ends can induce a contravariantly finite subcategory on the middle one.Then we apply our results to get some concrete covariantly finite and contravariantly finite subcategories on derived categories.