函子范畴与幂等完备化构造的相容性Compatibility of Functor Category and Idempotent Complete Construction
江维;陈清华;郑敏;
摘要(Abstract):
讨论函子范畴和范畴的幂等完备化构造的相容性,证明小范畴■到任意范畴■的函子范畴■的幂等完备化范畴等价于■到幂等完备化范畴■的函子范畴■.进一步得到函子范畴■是幂等完备的,当且仅当■是幂等完备的.
关键词(KeyWords): 幂等完备范畴;函子范畴;范畴等价
基金项目(Foundation): 国家自然科学基金资助项目(11871404)
作者(Authors): 江维;陈清华;郑敏;
参考文献(References):
- [1]MITCHELL B.Rings with several objects[J].Advances in Mathmatics,1972(8):1-161.
- [2]AUSLANDER M.Functors and morphisms determined by objects in representation theory of algebras[M].New York:Lecture Notes in Pure Appl,1978.
- [3]AUSLANDER M.Representation theory of artin algebras Ⅰ[J].Communications in Algebra,1974,1(3):77-268.
- [4]AUSLANDER M.Representation theory of artin algebras Ⅱ[J].Communications in Algebra,1974,1(4):269-310.
- [5]MARTINEZ-VOLLA R,ORTIZ-MORALES M.Tilting theory and functor categories Ⅰ(lassical tilting)[J].Applied Categorical Structures,2014,22(4):595-646.
- [6]MARTINEZ-VOLLA R,ORTIZ-MORALES M.Tilting theory and functor categories Ⅱ(generalized tilting)[J].Applied Categorical Structures,2013,21(4):311-348.
- [7]MARTINEZ-VOLLA R,ORTIZ-MORALES M.Tilting theory and functor categories Ⅲ(the Maps Category)[J].International Journal of Algebra,2011,5(11):529-561.
- [8]MAO L X.On homological dimensions in some functor categories[J].Mathematical Notes,2017(101):631–644.
- [9]OGAWA Y.Singular equivalences of functor categories via auslander-buchweitz approximations[J].Journal of Algebra,2020,546(15):734-752.
- [10]VAHED R.On the existence of recollements of functor categories[J].Communications in Algebra,2020,48(7):3133-3156.
- [11]陈清华,黄菊.加法范畴的回路范畴与η-扩张[J].福建师范大学学报(自然科学版),2017,33(3):1-4.
- [12]唐丽丹,沈臻.范畴的广义局部化[J].福州大学学报(自然科学版).2020,48(1):1-6.
- [13]周振强.导出等价与三角范畴的Abel化的一点注记[J].厦门大学学报(自然科学版).2013,52(5):585-589.
- [14]江维.关于函子范畴的一点注记[J].福建师范大学学报(自然科学版),2011,27(5):6-9.
- [15]FREYD P.Abelian categories[M].New York:Harper and Row,1964.