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Higher topos theory / Jacob Lurie.

By: Material type: TextTextSeries: Annals of mathematics studies ; no. 170.Publication details: Princeton, N.J. : Princeton University Press, 2009.Description: 1 online resource (xv, 925 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781400830558
  • 1400830559
  • 1282644955
  • 9781282644953
  • 9786612644955
  • 6612644958
Subject(s): Genre/Form: Additional physical formats: Print version:: Higher topos theory.DDC classification:
  • 512/.62 22
LOC classification:
  • QA169 .L87 2009eb
Other classification:
  • SI 830
  • SK 320
Online resources:
Contents:
Cover; Contents; Preface; Chapter 1. An Overview of Higher Category Theory; Chapter 2. Fibrations of Simplicial Sets; Chapter 3. The 8-Category of 8-Categories; Chapter 4. Limits and Colimits; Chapter 5. Presentable and Accessible 8-Categories; Chapter 6. 8-Topoi; Chapter 7. Higher Topos Theory in Topology; Appendix; Bibliography; General Index; Index of Notation.
Summary: 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 firs.
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Includes bibliographical references (pages 909-914) and indexes.

Print version record.

Cover; Contents; Preface; Chapter 1. An Overview of Higher Category Theory; Chapter 2. Fibrations of Simplicial Sets; Chapter 3. The 8-Category of 8-Categories; Chapter 4. Limits and Colimits; Chapter 5. Presentable and Accessible 8-Categories; Chapter 6. 8-Topoi; Chapter 7. Higher Topos Theory in Topology; Appendix; Bibliography; General Index; Index of Notation.

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 firs.

English.

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