The recollements induced by contravariantly finite subcategories

Let X be an admissible contravariantly finite subcategory of an abelian category A . We show that A has finite global X -resolution dimension if and only if there is a lower recollement of the homotopy category of bounded complexes over X . We also give sufficient conditions such that the recollemen...

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Bibliographic Details
Published in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2022-06, Vol.132 (1), Article 7
Main Authors: Hu, Yonggang, Yao, Hailou
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Let X be an admissible contravariantly finite subcategory of an abelian category A . We show that A has finite global X -resolution dimension if and only if there is a lower recollement of the homotopy category of bounded complexes over X . We also give sufficient conditions such that the recollement ( A , B , C ) of abelian categories can be lifted to a (lower or upper) recollement of relative derived categories with respect to balance pairs. Finally, we provide some applications.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-021-00649-0