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1、AGentleIntroductiontoCategoryTheory
2、thecalculationalapproach
3、MaartenM.FokkingaVersionofJune6,1994cM.M.Fokkinga,1992MaartenM.FokkingaUniversityofTwente,dept.INFPOBox217NL7500AEENSCHEDETheNetherlandse-mail:fokkinga@cs.utwente.nlContents0Introduction31Themainconcepts71aCategories::::::::::::::::
4、::::::::::::::::::::71bFunctors:::::::::::::::::::::::::::::::::::::131cNaturality::::::::::::::::::::::::::::::::::::191dAdjunctions:::::::::::::::::::::::::::::::::::261eDuality::::::::::::::::::::::::::::::::::::::292Constructionsincategories312aIso,epic,andmonic:::::::::::::::::::::::::::
5、::::312bInitialityand nality::::::::::::::::::::::::::::::342cProductsandSums:::::::::::::::::::::::::::::::382dCoequalisers:::::::::::::::::::::::::::::::::::432eColimits:::::::::::::::::::::::::::::::::::::47AMoreonadjointness59Chapters3and5of`LawandOrderinAlgorithmics'[4]presentacategorica
6、lapproachtoalgebras.Thosechap-tersdon'tusethenotionsofadjunctionandcolimit.SoyoumayskipSections1d,and2e,andAppendixAwhenyouareprimarilyinterestedinreadingthosechapters.12CONTENTSChapter0Introduction0.1Aim.Inthesenoteswepresenttheimportantnotionsfromcategorytheory.Theintentionistoprovideafairl
7、ygoodskillinmanipulatingwiththoseconceptsformally.Whatyouprobablywillnotacquirefromthesenotesistheabilitytorecognisetheconceptsinyourdailyworkwhenthatdi ersfromalgorithmics,sincewegiveonlyafewexamplesandthosearetakenfromalgorithmics.Forsuchanabilityyouneedtoworkthroughmany,verymanyexamples,in
8、diverse eldsofapplications.Thistextdi ersfrommostotherintroductionstocategorytheoryinthecalculationalstyleoftheproofs(especiallyinChapter2andAppendixA),therestrictiontoapplicationswithinalgorithmics,andtheomissionofmanyadditionalconceptsandfactsthatIconsidernothelpfulina rstintroductiontocate
9、gorytheory.0.2Acknowledgements.ThistextisacompilationandextensionofworkthatI'vedoneformythesis.Thatprojectwouldhavebeenafailurewithoutthehelporstimulationbymanypeople.Regardingthetechnicalcontents,RolandBackhouse,GrantMalcolm,LambertMeertensa
