The Resource Homotopy theory of higher categories, Carlos Simpson

Homotopy theory of higher categories, Carlos Simpson

Label
Homotopy theory of higher categories
Title
Homotopy theory of higher categories
Statement of responsibility
Carlos Simpson
Creator
Author
Subject
Language
eng
Summary
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
Member of
Cataloging source
UkCbUP
http://library.link/vocab/creatorDate
1962-
http://library.link/vocab/creatorName
Simpson, Carlos
Dewey number
512/.62
Index
index present
LC call number
QA612.7
LC item number
.S56 2012
Literary form
non fiction
Nature of contents
dictionaries
Series statement
New mathematical monographs
Series volume
19
http://library.link/vocab/subjectName
  • Homotopy theory
  • Categories (Mathematics)
Label
Homotopy theory of higher categories, Carlos Simpson
Link
https://doi.org/10.1017/CBO9780511978111
Instantiates
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. Operadic approaches; 5. Simplicial approaches; 6. Weak enrichment over a cartesian model category: an introduction -- Part II. Categorical Preliminaries: 7. Model categories; 8. Cell complexes in locally presentable categories; 9. Direct left Bousfield localization -- Part III. Generators and Relations: 10. Precategories; 11. Algebraic theories in model categories; 12. Weak equivalences; 13. Cofibrations; 14. Calculus of generators and relations; 15. Generators and relations for Segal categories -- Part IV. The Model Structure: 186 Sequentially free precategories; 17. Products; 18. Intervals; 19. The model category of M-enriched precategories -- Part V. Higher Category Theory: 20. Iterated higher categories; 21. Higher categorical techniques; 22. Limits of weak enriched categories; 23. Stabilization
Extent
1 online resource (xviii, 634 pages)
Form of item
online
Isbn
9780511978111
Isbn Type
(ebook)
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other physical details
digital, PDF file(s).
Specific material designation
remote
System control number
(UkCbUP)CR9780511978111
Label
Homotopy theory of higher categories, Carlos Simpson
Link
https://doi.org/10.1017/CBO9780511978111
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. Operadic approaches; 5. Simplicial approaches; 6. Weak enrichment over a cartesian model category: an introduction -- Part II. Categorical Preliminaries: 7. Model categories; 8. Cell complexes in locally presentable categories; 9. Direct left Bousfield localization -- Part III. Generators and Relations: 10. Precategories; 11. Algebraic theories in model categories; 12. Weak equivalences; 13. Cofibrations; 14. Calculus of generators and relations; 15. Generators and relations for Segal categories -- Part IV. The Model Structure: 186 Sequentially free precategories; 17. Products; 18. Intervals; 19. The model category of M-enriched precategories -- Part V. Higher Category Theory: 20. Iterated higher categories; 21. Higher categorical techniques; 22. Limits of weak enriched categories; 23. Stabilization
Extent
1 online resource (xviii, 634 pages)
Form of item
online
Isbn
9780511978111
Isbn Type
(ebook)
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other physical details
digital, PDF file(s).
Specific material designation
remote
System control number
(UkCbUP)CR9780511978111

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