LEADER 07349nam  2201897Ia 450 
001 9910784939903321
005 20230721015945.0
010   $a1-282-64495-5
010   $a9786612644955
010   $a1-4008-3055-9
024 7 $a10.1515/9781400830558
035   $a(CKB)2670000000032055
035   $a(EBL)557152
035   $a(OCoLC)781324677
035   $a(SSID)ssj0000409551
035   $a(PQKBManifestationID)11279733
035   $a(PQKBTitleCode)TC0000409551
035   $a(PQKBWorkID)10348413
035   $a(PQKB)10816198
035   $a(MiAaPQ)EBC557152
035   $a(DE-B1597)446962
035   $a(OCoLC)979881596
035   $a(OCoLC)990460716
035   $a(DE-B1597)9781400830558
035   $a(Au-PeEL)EBL557152
035   $a(CaPaEBR)ebr10435963
035   $a(CaONFJC)MIL264495
035   $a(EXLCZ)992670000000032055
100   $a20080828d2009      uy             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aHigher topos theory$b[electronic resource] /$fJacob Lurie
205   $aCourse Book
210   $aPrinceton, N.J. $cPrinceton University Press$d2009
215   $a1 online resource (944 p.)
225 1 $aAnnals of mathematics studies ;$vno. 170
300   $aDescription based upon print version of record.
311   $a0-691-14049-9 
311   $a0-691-14048-0 
320   $aIncludes bibliographical references and indexes.
327   $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. An Overview Of Higher Category Theory -- $tChapter Two. Fibrations Of Simplicial Sets -- $tChapter Three. The ?-Category Of ?-Categories -- $tChapter Four. Limits And Colimits -- $tChapter Five. Presentable And Accessible ?-Categories -- $tChapter Six. ?-Topoi -- $tChapter Seven. Higher Topos Theory In Topology -- $tAppendix -- $tBibliography -- $tGeneral Index -- $tIndex Of Notation
330   $aHigher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.
410  0$aAnnals of mathematics studies ;$vno. 170.
606   $aToposes
606   $aCategories (Mathematics)
610   $aAdjoint functors.
610   $aAssociative property.
610   $aBase change map.
610   $aBase change.
610   $aCW complex.
610   $aCanonical map.
610   $aCartesian product.
610   $aCategory of sets.
610   $aCategory theory.
610   $aCoequalizer.
610   $aCofinality.
610   $aCoherence theorem.
610   $aCohomology.
610   $aCokernel.
610   $aCommutative property.
610   $aContinuous function (set theory).
610   $aContractible space.
610   $aCoproduct.
610   $aCorollary.
610   $aDerived category.
610   $aDiagonal functor.
610   $aDiagram (category theory).
610   $aDimension theory (algebra).
610   $aDimension theory.
610   $aDimension.
610   $aEnriched category.
610   $aEpimorphism.
610   $aEquivalence class.
610   $aEquivalence relation.
610   $aExistence theorem.
610   $aExistential quantification.
610   $aFactorization system.
610   $aFunctor category.
610   $aFunctor.
610   $aFundamental group.
610   $aGrothendieck topology.
610   $aGrothendieck universe.
610   $aGroup homomorphism.
610   $aGroupoid.
610   $aHeyting algebra.
610   $aHigher Topos Theory.
610   $aHigher category theory.
610   $aHomotopy category.
610   $aHomotopy colimit.
610   $aHomotopy group.
610   $aHomotopy.
610   $aI0.
610   $aInclusion map.
610   $aInductive dimension.
610   $aInitial and terminal objects.
610   $aInverse limit.
610   $aIsomorphism class.
610   $aKan extension.
610   $aLimit (category theory).
610   $aLocalization of a category.
610   $aMaximal element.
610   $aMetric space.
610   $aModel category.
610   $aMonoidal category.
610   $aMonoidal functor.
610   $aMonomorphism.
610   $aMonotonic function.
610   $aMorphism.
610   $aNatural transformation.
610   $aNisnevich topology.
610   $aNoetherian topological space.
610   $aNoetherian.
610   $aO-minimal theory.
610   $aOpen set.
610   $aPower series.
610   $aPresheaf (category theory).
610   $aPrime number.
610   $aPullback (category theory).
610   $aPushout (category theory).
610   $aQuillen adjunction.
610   $aQuotient by an equivalence relation.
610   $aRegular cardinal.
610   $aRetract.
610   $aRight inverse.
610   $aSheaf (mathematics).
610   $aSheaf cohomology.
610   $aSimplicial category.
610   $aSimplicial set.
610   $aSpecial case.
610   $aSubcategory.
610   $aSubset.
610   $aSurjective function.
610   $aTensor product.
610   $aTheorem.
610   $aTopological space.
610   $aTopology.
610   $aTopos.
610   $aTotal order.
610   $aTransitive relation.
610   $aUniversal property.
610   $aUpper and lower bounds.
610   $aWeak equivalence (homotopy theory).
610   $aYoneda lemma.
610   $aZariski topology.
610   $aZorn's lemma.
615  0$aToposes.
615  0$aCategories (Mathematics)
676   $a512/.62
686   $aSI 830$2rvk
686   $aSK 320$2rvk
700   $aLurie$b Jacob$f1977-$0320628
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910784939903321
996   $aHigher topos theory$9784924
997   $aUNINA