摘要
We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause＇s work [Math. Ann., 2012, 353： 765-781]. Then we provide a criterion for the existence of recollement of derived categories of functor categories, which shows that the recollement structure may be induced by a proper morphism defined in finitely presented subcategories. This criterion is then used to construct a recollement of derived category of Gorenstein injective modules over CM-finite 2-Gorenstein artin algebras.
We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause＇s work [Math. Ann., 2012, 353： 765-781]. Then we provide a criterion for the existence of recollement of derived categories of functor categories, which shows that the recollement structure may be induced by a proper morphism defined in finitely presented subcategories. This criterion is then used to construct a recollement of derived category of Gorenstein injective modules over CM-finite 2-Gorenstein artin algebras.
基金
Acknowledgements The author would like to thank his supervisor Professor Zhaoyong Huang, for the valuable help, suggestions, guidance, and encouragement during his studies and preparation of this paper. He also thanks the referees for their careful reading and for pointing out related references. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11571164）.
