Higher topos theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2009]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 170 |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Main description: Higher 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 |
| Beschreibung: | 1 Online-Ressource (944 S.) |
| ISBN: | 9781400830558 |
| DOI: | 10.1515/9781400830558 |
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Datensatz im Suchindex
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| author | Lurie, Jacob 1977- |
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| author_sort | Lurie, Jacob 1977- |
| author_variant | j l jl |
| building | Verbundindex |
| bvnumber | BV042522502 |
| classification_rvk | SI 830 SK 320 |
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| ctrlnum | (OCoLC)1165605944 (DE-599)BVBBV042522502 |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400830558 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9781400830558 |
| language | English |
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| spelling | Lurie, Jacob 1977- (DE-588)139905529 aut Higher topos theory Princeton, N.J. Princeton University Press [2009] © 2009 1 Online-Ressource (944 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 170 Main description: Higher 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 Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Topos Mathematik (DE-588)4185717-3 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s Topos Mathematik (DE-588)4185717-3 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 978-0-691-14048-3 Annals of Mathematics Studies number 170 (DE-604)BV040389493 170 https://doi.org/10.1515/9781400830558?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400830558&searchTitles=true Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lurie, Jacob 1977- Higher topos theory Annals of Mathematics Studies Kategorientheorie (DE-588)4120552-2 gnd Topos Mathematik (DE-588)4185717-3 gnd |
| subject_GND | (DE-588)4120552-2 (DE-588)4185717-3 |
| title | Higher topos theory |
| title_auth | Higher topos theory |
| title_exact_search | Higher topos theory |
| title_full | Higher topos theory |
| title_fullStr | Higher topos theory |
| title_full_unstemmed | Higher topos theory |
| title_short | Higher topos theory |
| title_sort | higher topos theory |
| topic | Kategorientheorie (DE-588)4120552-2 gnd Topos Mathematik (DE-588)4185717-3 gnd |
| topic_facet | Kategorientheorie Topos Mathematik |
| url | https://doi.org/10.1515/9781400830558?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400830558&searchTitles=true |
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| work_keys_str_mv | AT luriejacob highertopostheory |