三角范疇局部化的若干注記.pdf

1、獨(dú)創(chuàng)性聲明本人聲明所呈交的學(xué)位論文是本人在導(dǎo)師指導(dǎo)下進(jìn)行的研究工作及取得的研究成果。據(jù)我所知，除了文中特別加以標(biāo)注和致謝的地方外，論文中不包含其他人已經(jīng)發(fā)表或撰寫過(guò)的研究成果，也不包含為獲得安徽大學(xué)或其他教育機(jī)構(gòu)的學(xué)位或證書而使用過(guò)的材料。與我一同工作的同志對(duì)本研究所做的任何貢獻(xiàn)均已在論文中作了明確的說(shuō)明并表示謝意。學(xué)位論文拓者簽名娌簽爭(zhēng)日期：矽心年多月s日學(xué)位論文版權(quán)使用授權(quán)書本學(xué)位論文作者完全了解安徽大學(xué)有關(guān)保留、使用學(xué)位論文的規(guī)定

2、，有權(quán)保留并向國(guó)家有關(guān)部門或機(jī)構(gòu)送交論文的復(fù)印件和磁盤，允許論文被查閱和借閱本人授權(quán)安徽大學(xué)可以將學(xué)位論文的全部或部分內(nèi)容編入有關(guān)數(shù)據(jù)庫(kù)進(jìn)行檢索，可以采用影印、縮印或掃描等復(fù)制手段保存、匯編學(xué)位論文。(保密的學(xué)位論文在解密后適用本授權(quán)書)學(xué)位論文作者簽名：“定磊簽字日期：細(xì)心年∥月)’日導(dǎo)師簽名：簽字日期：高茭芬細(xì)心年‘其孓琶ABSTRACTTriangulatedcategoriesplayanimportantroleinmanym

3、athematicalfields，suchasrepresentationtheoryofalgebras，algebraicgeometryandtopologyThelocalizationtheoryisanimportantwaytothestudyoftriangulatedcategoiesLetSbeacompatiblemultiplicativesystemofatriangulatedcategoryICandle

4、tS_1尼bethelocalizedcategoryof尼withrespecttosOntheotherhand，wedenotethesubcategory矽(s)=z∈瓦I3adistinguishtrianglex與Y_Zjx[1]st∈S、ItiswellknowthatSissaturatedifandonlyif妒(S)isathicktriangulatedsubcategory_However，ingeneral，妒

5、(S)maybenotatriangulatedsubcategoryInthisthesis，wemainlyinvestigatetherelationamonythepropertyofS，thelocalizedcategoryandthesubcategory妒(S)Thisthesisisorganizeda8followsInChapter1，webrieflyrecallthebackgroundandhistoryof

6、triangula，tedcategoriesandthelocalizationtheoryandthemainstructureofthisthesisChapter2dealswithsomebasicnotionsandsolnenecessarywellknownresults，includingtriangulatedcategories，trianglefunctors，multiplicativesystern，loea

7、lizationsofgeneralcategoriesandtriangulatedcategories，thicktriangulatedsubcategoriesandcompatiblemultiplicativesystemsInChapter3，westudythethickclosureoftriangulatedsubcategoriesandsaturatedclosureofcompatiblemultiplicat

8、ivesystem，andshowarelationbetweenthesaturatedclosureofamultiplicativesysteminducedbyatriangulatedsubcategoryandtheoneinducedbyitsthickclosureInChapter4，wegiveanewproofofawell—knowresult，iethereexistsaonetoonecorresponden