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1.
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关于L-fuzzifying TOP范畴
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张友 王书臣《数学季刊》,2003年第18卷第1期
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In this paper,the category of L-FTOP and the relations with the categories of TOP,Lα-FTOP are discussed.
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2.
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Cotilting modules with finite left perpendicular categories
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ZhiWei Li Pu Zhang《中国科学 数学(英文版)》,2012年第55卷第1期
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We characterize a cotilting module T such that the left perpendicular category ⊥ T is of finite type.
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3.
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From recollement of triangulated categories to recollement of abelian categories
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LIN YaNan & WANG MinXiong School of Mathematical Sciences Xiamen University Xiamen China School of Mathematical Sciences Huaqiao University Quanzhou《中国科学 数学(英文版)》,2010年第4期
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In this paper,we prove that if a triangulated category D admits a recollement relative to triangulated categories D' and D″,then the abelian category D/T admits a recollement relative to abelian categories D'/i(T) and D″/j(T) where T is a cluster tilting subcategory of D and satisfies i i (T) T,j j (T) T.
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4.
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On one-sided torsion pair
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Ya-nan LIN & Lin XIN Department of Mathematics Xiamen University Xiamen 361005 China Department of Mathematics Fujian Normal University Puzhou 350007 China《中国科学A辑(英文版)》,2007年第50卷第1期
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Motivated by the concept of a torsion pair in a pre-triangulated category induced by Beligiannis and Reiten, the notion of a left (right) torsion pair in the left (right) triangulated category is introduced and investigated. We provide new connections between different aspects of torsion pairs in one-sided triangulated categories, pre-triangulated categories, stable categories and derived categories.
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5.
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Abelianness of the “missing part” from a sheaf category to a module category
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CHEN JianMin LIN YaNan RUAN ShiQuan《中国科学 数学(英文版)》,2014年第57卷第2期
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This paper investigates the structure of the"missing part"from the category of coherent sheaves over a weighted projective line of weight type(2,2,n)to the category of finitely generated right modules on the associated canonical algebra.By constructing a t-structure in the stable category of the vector bundle category,we show that the"missing part"is equivalent to the heart of the t-structure,hence it is abelian.Moreover,it is equivalent to the category of finitely generated modules on the path algebra of type An-1.
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6.
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BGP reflection functors in root categories
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XIAO Jie ZHANG Guanglian1'2 & ZHU Bin Department of Mathematical Sciences Tsinghua University Beijing 100084 China Department of Mathematics Yancheng Teachers College Yancheng 224002 China《中国科学A辑(英文版)》,2005年第48卷第8期
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We define the BGP-reflection functors in the derived categories and the root categories. By Ringel's Hall algebra approach, the BGP-reflection functor is applicable to obtain the classical Weyl group action on the Lie algebra.
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7.
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本刊英文版2014年57卷第2期摘要
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《中国科学:数学》,2014年第2期
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New schemes with fractal error compensation for PDE eigenvalue computations;Abelianness of the ＂missing part＂ from a sheaf category to a module category;Totally compatible associative and Lie dialgebras, tridendriform algebras and PostLie algebras
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8.
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DIGRAPH CATEGORIES AND LINE DIGRAPH FUNCTORS
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张福基 李学良 黄琼湘 刘新《数学年刊B辑(英文版)》,1992年第3期
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The authors define line digraph functors on digraph category which are full and faith-ful and,as a consequence of the result,determine all homomorphisms in De Bruijn-Goodgraph category and automorphisms of Kautz digraph category.Moreover the authorsconsider a type of arc-full morphisms of digraph category such that F~n(f) is arc-full foreach functor F~n,and succeeding paper [9] study the strong homomorphisms of de Bruijn-Good digraph.
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9.
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广义直觉模糊集的范畴
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YANG Wan-cai LI Xiao-shen 《数学季刊》,2005年第20卷第2期
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In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS axe studied. Firstly， it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers， Secondly， it is proved that the category GIFS has middle object and consequently GIFS is a weak topos.Thirdly， by the use of theory of weak topos GIFS，the power object of an object in GIFS is studied.
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10.
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Stone's representation theorem in fuzzy topology
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刘应明 张德学《中国科学A辑(英文版)》,2003年第46卷第6期
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In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.
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11.
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Hom Functors from A Regular Category
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于永溪《数学研究与评论》,1986年第2期
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This paper aims to show the exactness of Hom functors with domain a regular category and codomain the category set. I°In [Ⅰ], we put forward a problem: To what degree and to which categories with ferminal objects can HAA (homological algebra in abelian categories)be naturally extended? By "naturally"we mean that the generalized theory degenerate into the theory of HAA when the terminal objects are nullS.
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12.
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TOPOLOGIES GENERATED BY FUNCTORS
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于永溪《数学研究与评论》,1986年第3期
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1. This note aims to introduce the notion of the categories with topologies and to discuss topologies generated by functors. A topological semigroup is a category with topologies, in addition, Propositions 10 and 11 will show the generated topologies compatible with adjoint equivalences and bijective half-functors (which are generalized inverse operations in an n-preadditive category, see [1]). Thus, we can believe that there are natural connections between topological and algebraic structures in category structure. In this direction, we shall propose several papers and this note will be an introduction of them.
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13.
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The double Ringel-Hall algebra on a hereditary abelian finitary length category
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DOU RuJing LIU QunHua & XIAO Jie Academy of Mathematics Systems Science Chinese Academy of Science Beijing China Institute for Algebra Number Theory University of Stuttgart Stuttgart Germany《中国科学 数学(英文版)》,2011年第2期
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In this paper, we study the category H (ρ) of semi-stable coherent sheaves of a fixed slope ρ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of H (ρ) and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves.
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14.
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Localization on certain Grothendieck categories
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F. Castaño-Iglesias N. Chifan C. Năstăsescu《数学学报(英文版)》,2009年第25卷第3期
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Using categorical techniques we obtain some results on localization and colocalization theory in Grothendieck categories with a set of small projective generators. In particular, we give a sufficient condition for such category to be semiartinian. For semiartinian Grothendieck categories where every simple object has a projective cover, we obtain that every localizing subcategory is a TTF-class. In addition, some applications to semiperfect categories are obtained.
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15.
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The Change-Base Issue for Ω-Categories
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Chengling FANG Dexue ZHANG《数学年刊B辑(英文版)》,2008年第29卷第4期
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Let G ： Ω→Ω＇ be a closed unital map between commutative, unital quantales. G induces a functor G^- from the category of Ω-categories to that of Ω＇-categories. This paper is concerned with some basic properties of G^-. The main results are： （1） when Ω, Ω＇ are integral, G ： Ω→Ω＇ and F ： Ω＇→Ω are closed unital maps, F is a left adjoint of G^- if and only if F is a left adjoint of G; （2） G^- is an equivalence of categories if and only if G is an isomorphism in the category of commutative unital quantales and closed unital maps; and （3） a sufficient condition is obtained for G^- to preserve completeness in the sense that GA is a complete Ω＇-category whenever A is a complete Ω-category.
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16.
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On the Category of Koszul Modules of Complexity One of an Exterior Algebra
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Jin Yun GUO Bing Jun LI Qiu Xian WU《数学学报(英文版)》,2006年第22卷第3期
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In this paper, we prove that there is a natural equivalence between the category F1（x） of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V of an m-dimensional vector space, and the category of the finite-dimensional locally nilpotent modules of the polynomial algebra of m - 1 variables.
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17.
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Yetter–Drinfeld Modules over Weak Braided Hopf Monoids and Center Categories
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Jos Nicanor ALONSO LVAREZ Ramón GONZLEZ RODRIGUEZ Carlos SONEIRA CALVO《数学学报(英文版)》,2014年第30卷第4期
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In this paper, we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter-Drinfeld modules over a weak braided Hopf monoid. We apply the general result to the calculus of the center in module categories.
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18.
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对偶的Hom型拟Hopf代数的余表示和范畴实现
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程永胜 宋光爱《数学研究及应用》,2015年第35卷第2期
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In this paper, we introduce the dual Hom-quasi-Hopf algebra and prove that the comodules category of a(braided) dual Hom-quasi-bialgebra is a monoidal category. Finally,we give a categorical realization of dual Hom-quasi-Hopf algebras.
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19.
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Quantaloid-enriched 范畴上的闭包算子与闭包系统
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刘敏 赵彬《数学研究及应用》,2013年第33卷第1期
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In this paper, we introduce the fundamental notions of closure operator and closure system in the framework of quantaloid-enriched category. We mainly discuss the relationship between closure operators and adjunctions and establish the one-to-one correspondence between closure operators and closure systems on quantaloid-enriched categories.
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20.
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偏倾斜模和倾斜模的分次与非分次性质
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郑敏 陈清华《数学研究及应用》,2009年第29卷第2期
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This paper gives the relationships among partial tilting objects （tilting objects） of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded partial tilting modules, there exist the Bongartz complements in the category of graded A-modules.
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