LEADER 03926nam 2200685Ia 450 001 9910459453503321 005 20200520144314.0 010 $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) 608 $aElectronic books. 615 0$aToposes. 615 0$aCategories (Mathematics) 676 $a512/.62 700 $aLurie$b Jacob$f1977-$0320628 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910459453503321 996 $aHigher topos theory$9784924 997 $aUNINA