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1、Inthelastfiftyyears,theuseofthenotionof'category'hasledtoaremarkableunificationandsimplificationofmathematics.Writtenbytwoofthebest-knownparticipantsinthisdevelopment,Conceptualmathe-maticsisthefirstbooktoapplycategoriestothemostelementarymathe-matics.Itthusservestwopurposes:toprovide
2、askeletonkeytomathematicsforthegeneralreaderorbeginningstudent;andtofurnishanintroductiontocategoriesforcomputerscientists,logicians,physicists,linguists,etc.whowanttogainsomefamiliaritywiththecategoricalmethod.Everyonewhowantstofollowtheapplicationsofmathematicstotwenty-firstcenturys
3、cienceshouldknowtheideasandtechniquesexplainedinthisbook.ConceptualMathematicsConceptualMathematicsAfirstintroductiontocategoriesF.WILLIAMLAWVEREStateUniversityofNewYorkatBuffaloSTEPHENH.SCHANUELStateUniversityofNewYorkatBuffaloCAMBRIDGEUNIVERSITYPRESSPUBLISHEDBYTHEPRESSSYNDICATEOFTHE
4、UNIVERSITYOFCAMBRIDGEThePittBuilding,TrumpingtonStreet,CambridgeCB21RP,UnitedKingdomCAMBRIDGEUNIVERSITYPRESSTheEdinburghBuilding,CambridgeCB22RU,UnitedKingdom40West20thStreet,NewYork,NY10011-4211,USA10StamfordRoad,Oakleigh,Melbourne3166,AustraliaCBuffaloWorkshopPress1991Italiantransla
5、tionC)FrancoMuzzio&c.editorespa1994ThiseditionCCambridgeUniversityPress1997Thisbookiscopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublished19
6、97PrintedintheUnitedKingdomattheUniversityPress,CambridgeAcataloguerecordforthisbookisavailablefromtheBritishLibraryLibraryofCongressCataloguinginPublicationdataLawvere,F.W.Conceptualmathematics:afirstintroductiontocategories/F.WilliamLawvereandStephenH.Schanuel.p.cm.Includesindex.ISB
7、N0-521-47249-0(hc).—ISBN0-521-47817-0(pb)1.Categories(Mathematics)I.Schanuel,S.H.(StephenHoel),1933–.II.title.QA169.L3551997511.3–dc2095-44725CIPISBN0521472490hardbackISBN0521478170paperbackContentsPleasereadthisxiiiNotetothereaderxvAcknowledgementsxviPreviewSession1Galileoandmultipli
8、catio
