As a generalization of tilting pair, which was introduced by Miyashita, the notion of silting pair is introduced in this paper. The authors extend a characterization of tilting modules given by Bazzoni to silting pair...As a generalization of tilting pair, which was introduced by Miyashita, the notion of silting pair is introduced in this paper. The authors extend a characterization of tilting modules given by Bazzoni to silting pairs, and prove that there is a one-to-one correspondence between equivalent classes of silting pairs and certain subcategories which satisfy some conditions.Furthermore, the authors also give a bijection between equivalent class of silting pairs and bounded above co-t-structure.展开更多
Let C be a triangulated category. We define m-term subcategories on C induced by n-rigid subcategories, which are extriangulated subcategories of C. Then we give a one-to-one correspondence between cotorsion pairs on ...Let C be a triangulated category. We define m-term subcategories on C induced by n-rigid subcategories, which are extriangulated subcategories of C. Then we give a one-to-one correspondence between cotorsion pairs on 2-term subcategories G and support τ-tilting subcategories on an abelian quotient of G. If an m-term subcategory is induced by a co-t-structure, then we have a one-to-one correspondence between cotorsion pairs on it and cotorsion pairs on C under certain conditions.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 11801004)the Top Talent Project of AHPU in 2020 (Grants No. S022021055)。
文摘As a generalization of tilting pair, which was introduced by Miyashita, the notion of silting pair is introduced in this paper. The authors extend a characterization of tilting modules given by Bazzoni to silting pairs, and prove that there is a one-to-one correspondence between equivalent classes of silting pairs and certain subcategories which satisfy some conditions.Furthermore, the authors also give a bijection between equivalent class of silting pairs and bounded above co-t-structure.
基金supported by the National Natural Science Foundation of China(Grant No.12171397)Panyue Zhou is supported by the National Natural Science Foundation of China(Grant No.12371034)by the Hunan Provincial Natural Science Foundation of China(Grant No.2023JJ30008)。
文摘Let C be a triangulated category. We define m-term subcategories on C induced by n-rigid subcategories, which are extriangulated subcategories of C. Then we give a one-to-one correspondence between cotorsion pairs on 2-term subcategories G and support τ-tilting subcategories on an abelian quotient of G. If an m-term subcategory is induced by a co-t-structure, then we have a one-to-one correspondence between cotorsion pairs on it and cotorsion pairs on C under certain conditions.
