Del 19 i serien New Mathematical Monographs

Homotopy Theory of Higher Categories

From Segal Categories to n-Categories and Beyond

Inbunden, Engelska, 2011

1 489 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.

Produktinformation

Utgivningsdatum2011-10-20
Mått158 x 235 x 38 mm
Vikt1 050 g
FormatInbunden
SpråkEngelska
SerieNew Mathematical Monographs
Antal sidor652
FörlagCambridge University Press
ISBN9780521516952

Tillhör följande kategorier

Topologi inom Naturvetenskap och teknik

Prologue; Acknowledgements; Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. The need for weak composition; 5. Simplicial approaches; 6. Operadic approaches; 7. Weak enrichment over a Cartesian model category: an introduction; Part II. Categorical Preliminaries: 8. Some category theory; 9. Model categories; 10. Cartesian model categories; 11. Direct left Bousfield localization; Part III. Generators and Relations: 12. Precategories; 13. Algebraic theories in model categories; 14. Weak equivalences; 15. Cofibrations; 16. Calculus of generators and relations; 17. Generators and relations for Segal categories; Part IV. The Model Structure: 18. Sequentially free precategories; 19. Products; 20. Intervals; 21. The model category of M-enriched precategories; 22. Iterated higher categories; Part V. Higher Category Theory: 23. Higher categorical techniques; 24. Limits of weak enriched categories; 25. Stabilization; Epilogue; References; Index.

Mer från samma författare

Current Developments in Hodge Theory

Phillip Griffiths, Ludmil Katzarkov, Carlos Simpson

Inbunden, 2026

3 289 kr

Del 1502

Asymptotic Behavior of Monodromy

Carlos Simpson

Häftad, 1991

369 kr

Mer från samma serie

Del 16

Lectures on Algebraic Cycles

Spencer Bloch

Inbunden, 2010

1 449 kr

Del 10

Monopoles and Three-Manifolds

Peter Kronheimer, Tomasz Mrowka

Häftad, 2010

1 619 kr

Del 2

Harmonic Measure

John B. Garnett, Donald E. Marshall

Inbunden, 2005

3 059 kr

Del 4

Heights in Diophantine Geometry

Enrico Bombieri, Walter Gubler

Häftad, 2007

1 509 kr

Del 2

Harmonic Measure

John B. Garnett, Donald E. Marshall

Häftad, 2008

1 619 kr

Del 13

Directed Algebraic Topology

Marco Grandis

Inbunden, 2009

2 939 kr

Del 12

Algebraic Methods in Unstable Homotopy Theory

Joseph Neisendorfer

Inbunden, 2010

3 609 kr

Del 15

Complex Multiplication

Reinhard Schertz

Inbunden, 2010

2 939 kr

Del 5

Combinatorics of Symmetric Designs

Yury J. Ionin, Mohan S. Shrikhande

Inbunden, 2006

3 369 kr

Del 1

Representation Theory of Finite Reductive Groups

Marc Cabanes, Michel Enguehard, Bela Bollobas

Inbunden, 2004

3 209 kr

Du kanske också är intresserad av

Current Developments in Hodge Theory

Phillip Griffiths, Ludmil Katzarkov, Carlos Simpson

Inbunden, 2026

3 289 kr

Del 1502

Asymptotic Behavior of Monodromy

Carlos Simpson

Häftad, 1991

369 kr

Ruth Kvarnström-Jones - Systrarna på Sophiahemmet, Inbunden

Nyhet

Del 3

Systrarna på Sophiahemmet

Ruth Kvarnström-Jones

Inbunden, 2026

299 kr329 kr

Del 29

Symplectic Topology and Floer Homology: Volume 2, Floer Homology and its Applications

Yong-Geun Oh

Inbunden, 2015

3 209 kr

Del 10

Monopoles and Three-Manifolds

Peter Kronheimer, Tomasz Mrowka

Inbunden, 2007

4 209 kr

Nyhet

Del 11

Medusa

Lars Kepler

Inbunden, 2026

289 kr319 kr

Del 4

Heights in Diophantine Geometry

Enrico Bombieri, Walter Gubler

Häftad, 2007

1 509 kr

Meromorphic Dynamics: Volume 2

Janina Kotus, Mariusz Urbański

Inbunden, 2023

2 419 kr

Del 2

Harmonic Measure

John B. Garnett, Donald E. Marshall

Häftad, 2008

1 619 kr

The Selberg Class of L-Functions

Jerzy Kaczorowski, Alberto Perelli

Inbunden, 2027

2 369 kr

Del 19 i serien New Mathematical Monographs

Homotopy Theory of Higher Categories

From Segal Categories to n-Categories and Beyond

Inbunden, Engelska, 2011

AvCarlos Simpson

1 489 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Produktinformation

Utgivningsdatum2011-10-20
Mått158 x 235 x 38 mm
Vikt1 050 g
FormatInbunden
SpråkEngelska
SerieNew Mathematical Monographs
Antal sidor652
FörlagCambridge University Press
ISBN9780521516952

Tillhör följande kategorier

Topologi inom Naturvetenskap och teknik

Prologue; Acknowledgements; Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. The need for weak composition; 5. Simplicial approaches; 6. Operadic approaches; 7. Weak enrichment over a Cartesian model category: an introduction; Part II. Categorical Preliminaries: 8. Some category theory; 9. Model categories; 10. Cartesian model categories; 11. Direct left Bousfield localization; Part III. Generators and Relations: 12. Precategories; 13. Algebraic theories in model categories; 14. Weak equivalences; 15. Cofibrations; 16. Calculus of generators and relations; 17. Generators and relations for Segal categories; Part IV. The Model Structure: 18. Sequentially free precategories; 19. Products; 20. Intervals; 21. The model category of M-enriched precategories; 22. Iterated higher categories; Part V. Higher Category Theory: 23. Higher categorical techniques; 24. Limits of weak enriched categories; 25. Stabilization; Epilogue; References; Index.