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In this paper we study recollements of abelian categories and balanced pairs. The main results are: recollements induce new balanced pairs from the middle category; the resolution dimensions are bounded under certain conditions. As an application, the resolution dimensions with respect to cotilting objects of abelian categories involved in recollements are recovered.
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참고문헌 (19)
참고문헌 신청
T. Aihara / 2014 / Dimensions of trian-gulated categories with respect to subcategories / J. Algebra 399:205~219
L. Angeleri Hugel / 2011 / Recollements and tilting objects / J. Pure Appl. Algebra 215(4):420~438
M. Auslander / 1991 / Applications of contravariantly finite subcategories / Adv. Math 86(1):111~152
M. Auslander / 1997 / Representation Theory of Artin Algebras / Cambridge University Press
M. Auslander / 1993 / Relative homology and representation theory. I. Relative homology and homologically finite subcategories / Comm. Algebra 21(9):2995~3031
L. Angeleri Hugel / 2011 / Recollements and tilting objects / J. Pure Appl. Algebra 215(4):420~438
M. Auslander / 1991 / Applications of contravariantly finite subcategories / Adv. Math 86(1):111~152
M. Auslander / 1997 / Representation Theory of Artin Algebras / Cambridge University Press
M. Auslander / 1993 / Relative homology and representation theory. I. Relative homology and homologically finite subcategories / Comm. Algebra 21(9):2995~3031
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