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1、基于柯西理想思义下的连续Q-domains赖洪亮四川大学数学学院，成都610064摘要：Q-范畴为研究量化domain理论提供了一个很好的棊本框架.本文在假设完备剩余格(Q,*)的承载格Q本身还是一个连续格的条件下，选収柯西理想描述定向完备性，引入了liminf完备的d范畴的连续性理论.在此基础Z上，进一步描述了waybelow关系，代数对象以及收缩等基木概念以及它们与连续性的关系.这些结果说明，这种连续的(2■范畴确实可以看做量化的连续domain.关键词：范畴论,liminf完备的Q-范畴，连续性，柯西网，柯西理想，伴随,waybelow关系中图分类号：0189
2、.13ContinuousdomainsbasedonCauchyidealsLAIHong-LiangDepartmentofMathematics,SichuanUniversity,Chengdu610064Abstract:Categoriesenrichedonacommutative,unitalquantalc(Q,*)makeagoodframeworkofquantitativedomaintheory.Inthispaper,foracompleteresiduatedlattice(Q,*)with(2beingacontinuouslatti
3、ce,anotionofcontinuityinliminfcompleteQ-categoriesisintroducedbasedonthedirectnessbeingdescribedbyCauchyideals・Moreover,thewaybelowrelations,algebraicobjectsandretractionsarccharacterizedandtherelationshipswithcontinuityisstudied.ItisshownthatcontinuousliminfcompleteQ-categoriescanbevi
4、ewedascontinuousQ-domains・Keywords:Categorytheory,liminfcompleteQ-category,continuity,Cauchynet,Cauchyideal,adjunction,waybelowrelation.0IntroductionAcompleteresiduatedlatticeisapair(Q,*)(alsodenotedQforshort),whereQisacompletelattice;*:QxQ—>Q,calledatensor,isacommutative,associativebi
5、naryoperationonQsuchthat(1)*ismonotoneoneachvariable,(2)ForeachpW(2,themonotonefunctionp*(一):(2>(2hasarightadjointp—>(一):Q>(2and(3)thetopelement1in(2isaunitelementfor*,i.e./?*1=〃foreveryp丘Q.Thebinaryoperation—►:QxQ—>Qgivenbyf(p,q)=pfq,iscalledthecotensor(correspondingto*)・垒金项口:NaturalS
6、cienceFoundationofChina(11101297),FundamentalResearchFoundationofSichuanUniversity(2010SCU21009)andDoctoralFundofMinistryofEducationofChina(20100I81120046)作者简介：Correspondenceauthor：LaiHongliang(I978-)・male,associateprofessor,majorresearchdirection：fuzzytopologyandfuzzyorder.Acompletere
7、siduatedlatticeisaspecialkindofsymmetricmonoidalclosedcompletesmallcategory.AcategoryenrichedoverQ,o『anQ-category,isasetAtogetherwithanassignmentofanelementA(a,b)WQtoeveryorderedpair(a,b)&彳xA.suchthat(1)1
