07349nam 2201897Ia 450 991081858320332120230721015945.01-282-64495-597866126449551-4008-3055-910.1515/9781400830558(CKB)2670000000032055(EBL)557152(OCoLC)781324677(SSID)ssj0000409551(PQKBManifestationID)11279733(PQKBTitleCode)TC0000409551(PQKBWorkID)10348413(PQKB)10816198(MiAaPQ)EBC557152(DE-B1597)446962(OCoLC)979881596(OCoLC)990460716(DE-B1597)9781400830558(Au-PeEL)EBL557152(CaPaEBR)ebr10435963(CaONFJC)MIL264495(EXLCZ)99267000000003205520080828d2009 uy 0engur|n|---|||||txtccrHigher topos theory[electronic resource] /Jacob LurieCourse BookPrinceton, N.J. Princeton University Press20091 online resource (944 p.)Annals of mathematics studies ;no. 170Description based upon print version of record.0-691-14049-9 0-691-14048-0 Includes bibliographical references and indexes. Frontmatter -- Contents -- Preface -- Chapter One. An Overview Of Higher Category Theory -- Chapter Two. Fibrations Of Simplicial Sets -- Chapter Three. The ∞-Category Of ∞-Categories -- Chapter Four. Limits And Colimits -- Chapter Five. Presentable And Accessible ∞-Categories -- Chapter Six. ∞-Topoi -- Chapter Seven. Higher Topos Theory In Topology -- Appendix -- Bibliography -- General Index -- Index Of NotationHigher 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.Annals of mathematics studies ;no. 170.ToposesCategories (Mathematics)Adjoint functors.Associative property.Base change map.Base change.CW complex.Canonical map.Cartesian product.Category of sets.Category theory.Coequalizer.Cofinality.Coherence theorem.Cohomology.Cokernel.Commutative property.Continuous function (set theory).Contractible space.Coproduct.Corollary.Derived category.Diagonal functor.Diagram (category theory).Dimension theory (algebra).Dimension theory.Dimension.Enriched category.Epimorphism.Equivalence class.Equivalence relation.Existence theorem.Existential quantification.Factorization system.Functor category.Functor.Fundamental group.Grothendieck topology.Grothendieck universe.Group homomorphism.Groupoid.Heyting algebra.Higher Topos Theory.Higher category theory.Homotopy category.Homotopy colimit.Homotopy group.Homotopy.I0.Inclusion map.Inductive dimension.Initial and terminal objects.Inverse limit.Isomorphism class.Kan extension.Limit (category theory).Localization of a category.Maximal element.Metric space.Model category.Monoidal category.Monoidal functor.Monomorphism.Monotonic function.Morphism.Natural transformation.Nisnevich topology.Noetherian topological space.Noetherian.O-minimal theory.Open set.Power series.Presheaf (category theory).Prime number.Pullback (category theory).Pushout (category theory).Quillen adjunction.Quotient by an equivalence relation.Regular cardinal.Retract.Right inverse.Sheaf (mathematics).Sheaf cohomology.Simplicial category.Simplicial set.Special case.Subcategory.Subset.Surjective function.Tensor product.Theorem.Topological space.Topology.Topos.Total order.Transitive relation.Universal property.Upper and lower bounds.Weak equivalence (homotopy theory).Yoneda lemma.Zariski topology.Zorn's lemma.Toposes.Categories (Mathematics)512/.62SI 830rvkSK 320rvkLurie Jacob1977-320628MiAaPQMiAaPQMiAaPQBOOK9910818583203321Higher topos theory784924UNINA