In this paper,we study the relationship of balanced pairs in a recollement.As an application of balanced pairs,we introduce the notion of the relative tilting objects,and give a characterization of relative tilting ob...In this paper,we study the relationship of balanced pairs in a recollement.As an application of balanced pairs,we introduce the notion of the relative tilting objects,and give a characterization of relative tilting objects,which is similar to Bazzoni characterization of n-tilting modules.Finally,we investigate the relationship of relative tilting objects in a recollement.展开更多
Let C=(C,E,s)be an extriangulated category.In this paper,we give the notion of ideal balanced pairs in C and some equivalent characterizations of ideal balanced pairs.We show that there is a one-to-one correspondence ...Let C=(C,E,s)be an extriangulated category.In this paper,we give the notion of ideal balanced pairs in C and some equivalent characterizations of ideal balanced pairs.We show that there is a one-to-one correspondence between balanced pairs and ideal balanced pairs satisfying certain conditions when C is of a negative first extension.We also prove that there is a bijective correspondence between ideal balanced pairs(I,J)and additive subfunctors F■E with enough projective morphisms and enough injective morphisms in C.展开更多
Let(X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to(X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or ...Let(X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to(X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the X-resolution dimension of Y(resp. Y-coresolution dimension of X)is finite, then the bounded homotopy category of Y(resp. X) is contained in that of X(resp. Y). As a consequence, we get that the right X-singularity category coincides with the left Y-singularity category if the X-resolution dimension of Y and the Y-coresolution dimension of X are finite.展开更多
Let C be a triangulated category.We first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classesξwith enoughξ-projectives andξ-injectiv...Let C be a triangulated category.We first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classesξwith enoughξ-projectives andξ-injectives.Assume thatξ:=ξX=ξ^(Y) is the proper class induced by a balanced pair(X,Y).We prove that(C,Eξ,sξ)is an extriangulated category.Moreover,it is proved that(C,Eξ,sξ)is a triangulated category if and only if X=Y=0,and that(C,Eξ,sξ)is an exact category if and only if X=Y=C.As an application,we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.展开更多
In Enochs'relative homological dimension theory occur the(co)resolvent and(co)proper dimensions,which are defined by proper and coproper resolutions constructed by precovers and preenvelopes,respectively.Recently,...In Enochs'relative homological dimension theory occur the(co)resolvent and(co)proper dimensions,which are defined by proper and coproper resolutions constructed by precovers and preenvelopes,respectively.Recently,some authors have been interested in relative homological dimensions defined by just exact sequences.In this paper,we contribute to the investigation of these relative homological dimensions.First we study the relation between these two kinds of relative homological dimensions and establish some transfer results under adjoint pairs.Then relative global dimensions are studied,which lead to nice characterizations of some properties of particular cases of self-orthogonal subcategories.At the end of this paper,relative derived functors are studied and generalizations of some known results of balance for relative homology are established.展开更多
We introduce and study the relative lett derive functor Torn（￡,￡1） category, which unifies several related left derived functors. Then we give some criteria for computing the -resolution dimensions of modules in t...We introduce and study the relative lett derive functor Torn（￡,￡1） category, which unifies several related left derived functors. Then we give some criteria for computing the -resolution dimensions of modules in terms of the properties of Torn（￡,￡1） . We also construct a complete and hereditary cotorsion pair relative to balanced pairs. Some known results are obtained as corollaries.展开更多
Entity matching that aims at finding some records belonging to the same real-world objects has been studied for decades. In order to avoid verifying every pair of records in a massive data set, a common method, known ...Entity matching that aims at finding some records belonging to the same real-world objects has been studied for decades. In order to avoid verifying every pair of records in a massive data set, a common method, known as the blocking- based method, tends to select a small proportion of record pairs for verification with a far lower cost than O（n2）, where n is the size of the data set. Furthermore, executing multiple blocking functions independently is critical since much more matching records can be found in this way, so that the quality of the query result can be improved significantly. It is popular to use the MapReduce （MR） framework to improve the performance and the scalability of some compli- cated queries by running a lot of map （/reduce） tasks in parallel. However, entity matching upon the MapReduce frame- work is non-trivial due to two inevitable challenges： load balancing and pair deduplication. In this paper, we propose a novel solution, called M rEin, to handle these challenges with the support of multiple blocking functions. Although the existing work can deal with load balancing and pair deduplication respectively, it still cannot deal with both challenges at the same time. Theoretical analysis and experimental results upon real and synthetic data sets illustrate the high effectiveness and efficiency of our proposed solutions.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11801004,12101003 and 12271249)the Natural Science Foundation of Universities of Anhui(Grant No.2023AH050950)+2 种基金the Top talent project of AHPU in 2020(Grant No.S022021055)the Natural Science Foundation of Anhui province(Grant No.2108085QA07)the Startup Foundation for Introducing Talent of AHPU(Grant No.2020YQQ067)。
文摘In this paper,we study the relationship of balanced pairs in a recollement.As an application of balanced pairs,we introduce the notion of the relative tilting objects,and give a characterization of relative tilting objects,which is similar to Bazzoni characterization of n-tilting modules.Finally,we investigate the relationship of relative tilting objects in a recollement.
基金supported by National Natural Science Foundation of China(Grant No.12071064)Natural Science Foundation of Jilin Province of China(Grant No.YDZJ202101ZYTS168)。
文摘Let C=(C,E,s)be an extriangulated category.In this paper,we give the notion of ideal balanced pairs in C and some equivalent characterizations of ideal balanced pairs.We show that there is a one-to-one correspondence between balanced pairs and ideal balanced pairs satisfying certain conditions when C is of a negative first extension.We also prove that there is a bijective correspondence between ideal balanced pairs(I,J)and additive subfunctors F■E with enough projective morphisms and enough injective morphisms in C.
基金supported by National Natural Science Foundation of China(Grant No.11171142)
文摘Let(X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to(X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the X-resolution dimension of Y(resp. Y-coresolution dimension of X)is finite, then the bounded homotopy category of Y(resp. X) is contained in that of X(resp. Y). As a consequence, we get that the right X-singularity category coincides with the left Y-singularity category if the X-resolution dimension of Y and the Y-coresolution dimension of X are finite.
基金Xianhui Fu was supported by YDZJ202101ZYTS168 and the NSF of China(12071064)Jiangsheng Hu was supported by the NSF of China(12171206)+2 种基金the Natural Science Foundation of Jiangsu Province(BK20211358)Haiyan Zhu was supported by Zhejiang Provincial Natural Science Foundation of China(LY18A010032)the NSF of China(12271481).
文摘Let C be a triangulated category.We first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classesξwith enoughξ-projectives andξ-injectives.Assume thatξ:=ξX=ξ^(Y) is the proper class induced by a balanced pair(X,Y).We prove that(C,Eξ,sξ)is an extriangulated category.Moreover,it is proved that(C,Eξ,sξ)is a triangulated category if and only if X=Y=0,and that(C,Eξ,sξ)is an exact category if and only if X=Y=C.As an application,we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.
基金The second and fourth authors were partially supported by the grant MTM2014-54439-P from Ministerio de Economia y CompetitividadThe third author was partially supported by NSFC(11771202).
文摘In Enochs'relative homological dimension theory occur the(co)resolvent and(co)proper dimensions,which are defined by proper and coproper resolutions constructed by precovers and preenvelopes,respectively.Recently,some authors have been interested in relative homological dimensions defined by just exact sequences.In this paper,we contribute to the investigation of these relative homological dimensions.First we study the relation between these two kinds of relative homological dimensions and establish some transfer results under adjoint pairs.Then relative global dimensions are studied,which lead to nice characterizations of some properties of particular cases of self-orthogonal subcategories.At the end of this paper,relative derived functors are studied and generalizations of some known results of balance for relative homology are established.
基金Supported by NSFC(Grant Nos.11171142,11571164)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘We introduce and study the relative lett derive functor Torn（￡,￡1） category, which unifies several related left derived functors. Then we give some criteria for computing the -resolution dimensions of modules in terms of the properties of Torn（￡,￡1） . We also construct a complete and hereditary cotorsion pair relative to balanced pairs. Some known results are obtained as corollaries.
基金Acknowledgements Our research is supported by the National Basic Research Program of China （2012CB316203）, the National Natural Science Foundation of China （Grant Nos. 61370101 and U1501252）, Shanghai Knowledge Service Platform Project （ZF1213）, and Innovation Program of Shanghai Municipal Education Commission （14ZZ045）.
文摘Entity matching that aims at finding some records belonging to the same real-world objects has been studied for decades. In order to avoid verifying every pair of records in a massive data set, a common method, known as the blocking- based method, tends to select a small proportion of record pairs for verification with a far lower cost than O（n2）, where n is the size of the data set. Furthermore, executing multiple blocking functions independently is critical since much more matching records can be found in this way, so that the quality of the query result can be improved significantly. It is popular to use the MapReduce （MR） framework to improve the performance and the scalability of some compli- cated queries by running a lot of map （/reduce） tasks in parallel. However, entity matching upon the MapReduce frame- work is non-trivial due to two inevitable challenges： load balancing and pair deduplication. In this paper, we propose a novel solution, called M rEin, to handle these challenges with the support of multiple blocking functions. Although the existing work can deal with load balancing and pair deduplication respectively, it still cannot deal with both challenges at the same time. Theoretical analysis and experimental results upon real and synthetic data sets illustrate the high effectiveness and efficiency of our proposed solutions.
