(24) (New Mathematical Monographs) Emily Riehl-Categorical Homotopy Theory-Cambridge University Press (2014).pdf

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1、CategoricalHomotopyTheoryThisbookdevelopsabstracthomotopytheoryfromthecategoricalperspective,withaparticularfocusonexamples.PartIdiscussestwocompetingperspectivesbywhichonetypicallyfirstencountershomotopy(co)limits:eitherasderivedfunctorsdefin-ablewhentheappropriatediagramcategorie

2、sadmitcompatiblemodelstructuresorthroughparticularformulaethatgivetherightnotionincertainexamples.Riehlunifiestheseseeminglyrivalperspectivesanddemonstratesthatmodelstructuresondiagramcategoriesareunnecessary.Homotopy(co)limitsareexplainedtobeaspecialcaseofweighted(co)limits,afoun

3、dationaltopicinenrichedcategorytheory.InPartII,Riehlfurtherexaminesthistopic,separatingcategoricalargumentsfromhomotopicalones.PartIIItreatsthemostubiquitousaxiomaticframeworkforhomotopytheory–Quillen’smodelcategories.HereRiehlsimplifiesfamiliarmodelcategoricallemmasanddefini-tions

4、byfocusingonweakfactorizationsystems.PartIVintroducesquasi-categoriesandhomotopycoherence.EmilyRiehlisaBenjaminPeirceFellowintheDepartmentofMathematicsatHarvardUniversityandaNationalScienceFoundationMathematicalSciencesPost-doctoralResearchFellow.NEWMATHEMATICALMONOGRAPHSEditoria

5、lBoardBelaBollob´as,WilliamFulton,AnatoleKatok,´FrancesKirwan,PeterSarnak,BarrySimon,BurtTotaroAllthetitleslistedbelowcanbeobtainedfromgoodbooksellersorfromCambridgeUniversityPress.Foracompleteserieslistingvisitwww.cambridge.org/mathematics.1.M.CabanesandM.EnguehardRepresentation

6、TheoryofFiniteReductiveGroups2.J.B.GarnettandD.E.MarshallHarmonicMeasure3.P.CohnFreeIdealRingsandLocalizationinGeneralRings4.E.BombieriandW.GublerHeightsinDiophantineGeometry5.Y.J.IoninandM.S.ShrikhandeCombinatoricsofSymmetricDesigns6.S.Berhanu,P.D.Cordaro,andJ.HounieAnIntroducti

7、ontoInvolutiveStructures7.A.ShlapentokhHilbertsTenthProblem8.G.MichlerTheoryofFiniteSimpleGroupsI9.A.BakerandG.Wustholz¨LogarithmicFormsandDiophantineGeometry10.P.KronheimerandT.MrowkaMonopolesandThree-Manifolds11.B.Bekka,P.delaHarpe,andA.ValetteKazhdansProperty(T)12.J.Neisendorf

8、erAlgebraicMethodsinUnstableHomotopyTheo