Category Theory for Scientists

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1、CategoryTheoryforScientists(OldVersion)DavidI.SpivakSeptember17,2013an#observa*on#when#executed#analyzed#by#a#results#in#person#yields#an#experiment#a#hypothesis#mo*vates#the#analyzed#by#a#specifica*on#of#person#produces#a#predic*on#Howcanmathematicsmakethisdiagram

2、meaningful?2PrefaceAnearlyversionofthisbookwasputonlineinFebruary2013toserveasthetextbookformycourseCategoryTheoryforScientiststaughtinthespringsemesterof2013atMIT.Duringthatsemester,studentsprovidedmewithhundredsofcommentsandquestions,whichledtoasubstantialimprov

3、ement(andtheadditionof50pages)totheoriginaldocument.Inthesummerof2013IsignedacontractwiththeMITPresstopublishanewversionofthisworkunderthetitleCategoryTheoryfortheSciences.BecauseIamcommittedtotheopensourcedevelopmentmodelIinsistedthataversionofthisbook,namelytheo

4、neyouarereading,remainfreelyavailableonline.TheMITPressversionwillofcoursenotbefree.Otherthanthetitle,therearetwomaindifferencesbetweenthepresentversionandtheMITPressversion.ThefirstdifferenceisthatIwilldoafulleditwiththehelpofprofessionaleditorsfromthePress.Thesecon

5、ddifferenceisthatIwillwriteupsolutionstothebook’s(approximately280)exercises;someofthesewillbeincludedinthepublishedversion,whereastherestwillbeavailablebywayofapassword-protectedpage,accessibleonlytoprofessorswhoteachthesubject.34Contents1Introduction71.1Abriefhis

6、toryofcategorytheory.......................91.2Intentionofthisbook.............................101.3Whatisrequestedfromthestudent......................121.4Categorytheoryreferences...........................121.5Acknowledgments................................122Th

7、ecategoryofsets152.1Setsandfunctions...............................152.2Commutativediagrams............................222.3Ologs......................................232.4Productsandcoproducts............................322.5FinitelimitsinSet.....................

8、..........412.6FinitecolimitsinSet.............................492.7OthernotionsinSet..............................563Categoriesandfunctors,withoutadmit