David I. Spivak-Category Theory for the Sciences-The MIT Press (2014).pdf

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1、CategoryTheoryfortheSciencesCategoryTheoryfortheSciencesDavidI.SpivakTheMITPressCambridge,MassachusettsLondon,Englandc2014MassachusettsInstituteofTechnologyAllrightsreserved.Nopartofthisbookmaybereproducedinanyformbyanyelec-tronicormechanicalmeans(in

2、cludingphotocopying,recording,orinformationstorageandretrieval)withoutpermissioninwritingfromthepublisher.MITPressbooksmaybepurchasedatspecialquantitydiscountsforbusinessorsalespromotionaluse.Forinformation,pleaseemailspecialsales@mitpress.mit.edu.Lib

3、raryofCongressCataloging-in-PublicationDataSpivak,DavidI.,1978–author.Categorytheoryforthesciences/DavidI.Spivak.pagescmIncludesbibliographicalreferencesandindex.ISBN978-0-262-02813-4(hardcover:alk.paper)1.Science—Mathematicalmodels.2.Categories(Mathe

4、matics)I.Title.Q175.32.M38S652014512’.62—dc23201400721510987654321Contents1Introduction11.1Abriefhistoryofcategorytheory.......................41.2Intentionofthisbook.............................51.3Whatisrequestedfromthestudent......................7

5、1.4Categorytheoryreferences...........................72TheCategoryofSets92.1Setsandfunctions...............................92.2Commutativediagrams............................232.3Ologs......................................243FundamentalConsiderations

6、inSet413.1Productsandcoproducts............................413.2FinitelimitsinSet...............................553.3FinitecolimitsinSet.............................753.4OthernotionsinSet..............................904CategoriesandFunctors,WithoutAd

7、mittingIt1154.1Monoids.....................................1164.2Groups......................................1404.3Graphs......................................1464.4Orders......................................1624.5Databases:schemasandinstances.......

8、...............1845BasicCategoryTheory2035.1Categoriesandfunctors............................2035.2Commoncategoriesandfunctorsfrompuremath..............2395.3Naturaltransformations............................267vviCONTENTS5.4Categoriesandschem