Basic Category Theory (Cambridge Studies in Advanced Mathematics) [Tom Leinster].pdf

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1、CAMBRIDGESTUDIESINADVANCEDMATHEMATICS143EditorialBoardB.BOLLOBÁS,W.FULTON,A.KATOK,F.KIRWAN,P.SARNAK,B.SIMON,B.TOTAROBASICCATEGORYTHEORYAttheheartofthisshortintroductiontocategorytheoryistheideaofauniversalprop-erty,importantthroughoutmathematics.Afteranintroductorychaptergivingthebasicdefinition

2、s,separatechaptersexplainthreewaysofexpressinguniversalproperties:viaadjointfunctors,representablefunctorsandlimits.Afinalchaptertiesallthreetogether.Thebookissuitableforuseincoursesorforindependentstudy.Assumingrelativelylittlemathematicalbackground,itisidealforbeginninggraduatestudentsoradvanc

3、edundergraduateslearningcategorytheoryforthefirsttime.Foreachnewcategoricalconcept,ageneroussupplyofexamplesisprovided,takenfromdifferentpartsofmath-ematics.Atpointswheretheleapinabstractionisparticularlygreat(suchastheYonedalemma),thereaderwillfindcarefulandextensiveexplanations.Copiousexercises

4、areincluded.TomLeinsterhasheldpostdoctoralpositionsatCambridgeandtheInstitutdesHautesÉtudesScientifiques(France),andheldanEPSRCAdvancedResearchFellowshipattheUniversityofGlasgow.HeiscurrentlyaChancellor’sFellowattheUniversityofEdinburgh.HeisalsotheauthorofHigherOperads,HigherCategories(Cambridge

5、UniversityPress,2004),andoneofthehostsoftheresearchblog,Then-CategoryCafé.CAMBRIDGESTUDIESINADVANCEDMATHEMATICSEditorialBoard:B.Bollobás,W.Fulton,A.Katok,F.Kirwan,P.Sarnak,B.Simon,B.TotaroAllthetitleslistedbelowcanbeobtainedfromgoodbooksellersorfromCambridgeUniversityPress.Foracompleteserieslis

6、tingvisit:www.cambridge.org/mathematics.Alreadypublished107K.KodairaComplexanalysis108T.Ceccherini-Silberstein,F.Scarabotti&F.TolliHarmonicanalysisonfinitegroups109H.GeigesAnintroductiontocontacttopology110J.FarautAnalysisonLiegroups:Anintroduction111E.ParkComplextopologicalK-theory112D.W.Strooc

7、kPartialdifferentialequationsforprobabilists113A.Kirillov,JrAnintroductiontoLiegroupsandLiealgebras114F.Gesztesyetal.Solitonequationsandtheiralgebro-geometricsolutions,II115E.deFaria&W.deMeloMathematicaltoolsforone-dimensionaldyna