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1、BRICSBRICSLS-95-1J.vanOosten:BasicCategoryTheoryBasicResearchinComputerScienceBasicCategoryTheoryJaapvanOostenBRICSLectureSeriesLS-95-1ISSN1395-2048January1995Copyrightc1995,BRICS,DepartmentofComputerScienceUniversityofAarhus.Allrightsreserved.Reproductionofallorpartofthisworkispermittedforeduca
2、tionalorresearchuseonconditionthatthiscopyrightnoticeisincludedinanycopy.SeebackinnerpageforalistofrecentpublicationsintheBRICSLectureSeries.Copiesmaybeobtainedbycontacting:BRICSDepartmentofComputerScienceUniversityofAarhusNyMunkegade,building540DK-8000AarhusCDenmarkTelephone:+4589423360Telefax:
3、+4589423255Internet:BRICS@daimi.aau.dkBRICSpublicationsareingeneralaccessiblethroughWWWandanonymousFTP:http://www.brics.aau.dk/BRICS/ftpftp.brics.aau.dk(cdpub/BRICS)BasicCategoryTheoryJaapvanOostenJaapvanOosten1BRICSDepartmentofComputerScienceUniversityofAarhusNyMunkegadeDK-8000AarhusC,Denmark1B
4、asicResearchInComputerScience,CentreoftheDanishNationalResearchFoundation.PrefaceThesenotescontainthematerialofashortcourseoncategoriesIgaveinArhusintheautumnof1994,aspartofGlynnWinskel'ssemanticscourse.Lateron,whilewriting,Iaddedsomematerial,butnotmuch.Thestyleinwhichtheyarewrittenre
ectsmyvie
5、woncategorytheory:itis,especiallyatthislowlevel,practiceratherthantheorywhichcounts.Ihavethereforegivenmanyproofsasexercises.Ifyoureallywanttogetagriponthesubject,Istronglysuggestyoudoasmanyofthemasyoucan.Thesamegoesfortheexamples.Theyarethe
eshandbonesofthetheory,andmanyofthemhavebeenchosensoth
6、eyarearecurringthemefunctorso/maybegivenasexamplesinchapter1,beshowntoconstituteanCDadjunctioninchapter5,whilethismayturnouttobeamonadicsituationinchapter6.Forthesamereason,referencesareomitted.Evenasketchyproof,orahintofthecrucialargument,isbetterthananintimidatingreferenceto[R].Ofcourse,theex
7、ampleswillbebestunderstoodbystudentswhoarefamiliarwiththemathematicalnotionsinvolved,butingeneralthesenotesdonotrequirealotofmathematicalbackground,exceptforsomebasicknowledgeofgroups,ringsandtopologicalspaces(althoughexampl
