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ID:28356601
大小:7.65 MB
页数:115页
时间:2018-12-09
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1、1L福建师范大学李德梅博士学位论文AbstractExactcategoryisnotonlythefoundationofAbeliancategorybutalsoitsnat-uralgeneralization.Sincelast50sor60s,expertsandauthorshavestudiedexactcategories,especiallyintheonesbasedonadditivecategoriescommonlyattributedtoQuillen,whichhave
2、playedallimportantroleinalgebraicK—theory,therepresen-^tationtheory,categorytheory,etc.Theclassofexactcategories,whoseadmissiblemonomorphismsareclosedunderpull-backs,isinvestigatedinthethesis.These-eXauctcategoriescanbecommonlyfoundintorsiontheoryandthe
3、yareexactlydif-ferentfromabeliancategories.Inthisthesis,wecharacterizethelatticestructuresofpull-backexactcategorriesandalsogiveastudyonequivalenceanduniversalpropertitiesofthelocalizationsofmodularpull-backexactcategories.Atthebeginningofthethesis,wema
4、keareviewontheresearches,explorethetrendsrelatedtothisthesis,sumupthegroundworkandgivesomenotationspresentedinthethesis.Thethesisisdividedintofourchapters.Chapterone:Wefirstintroducethenotionofpull-backexactcategoryandgivesomedescriptionsofitsbasicprope
5、rties.Thenwegivesomeexmnplestoillustratetheexistenceoftheseexactcategories.Wealsoshowtheexistenceofnon—abelianpull-backexactcategories.Atlast,westudytherecollementsofpuU-backexactcategories.Chaptertwo:Thelatticestructuresonapull-backexactcategoryareinve
6、sti-gated.Usingadmissiblemonomorphismsandadmissibleepimorphisms,wedefinetwoclassesofmodularlattices(E,V,八)and(E,V,八),andshowtheexistenceofalatticeisomorphismbetweenthesetwoclasses.Wealsousedistributiveelementstocharacterizelatticecategoryonapullbackexac
7、tcategoryandthenweobtainexactstructuresofalatticecategoryinducedbythoseofapull-backexactcategory.Chapterthree:WeuseSerreclassesanddirectlimitstodefinetwoclassesofIIlocalizationcategoriesofmodularpull-backexactcategories,respectively,andshowthesetwoclass
8、esareequivalent.Chapterfour:Wegiveafurtherstudyon.thelocalizationofmodularpuu-backexactcategoriesunderuniversalproperties.Keywords:exactcategory,(modular)pull-backexactcategory,lattice,Rec-ollement,localization,Serreclass,directl
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