Coherence in three-dimensional category theory /:
"Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence theorem, of which this book provides a definitive treatment, as well as covering related results....
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2013.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
201. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence theorem, of which this book provides a definitive treatment, as well as covering related results. Along the way the author treats such material as the Gray tensor product and gives a construction of the fundamental 3-groupoid of a space. The book serves as a comprehensive introduction, covering essential material for any student of coherence and assuming only a basic understanding of higher category theory. It is also a reference point for many key concepts in the field and therefore a vital resource for researchers wishing to apply higher categories or coherence results in fields such as algebraic topology or theoretical computer science"-- "In the study of higher categories, dimension three occupies an interesting position on the landscape of higher dimensional category theory. From the perspective of a "hands-on" approach to defining weak n-categories, tricategories represent the most complicated kind of higher category that the community at large seems comfortable working with."-- |
| Beschreibung: | 1 online resource (vii, 278 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781107336896 1107336899 9781139542333 1139542338 9781107327139 110732713X 9781107333574 1107333571 1107238420 9781107238428 1299399959 9781299399952 1107336066 9781107336063 |
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| author | Gurski, Nick, 1980- |
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| contents | Introduction -- Background: Bicategorical background ; Coherence for bicategories ; Gray-categories -- Tricategories: The algebraic definition of tricategory ; Examples ; Free constructions ; Basic structure ; Gray-categories and tricategories ; Coherence via Yoneda ; Coherence via free constructions -- Gray-monads: Codescent in Gray-categories ; Codescent as a weighted colimit ; Gray-monads and their algebras ; The reflection of lax algebras into strict algebras ; A general coherence result. |
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| discipline | Mathematik |
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| indexdate | 2024-11-27T13:25:13Z |
| institution | BVB |
| isbn | 9781107336896 1107336899 9781139542333 1139542338 9781107327139 110732713X 9781107333574 1107333571 1107238420 9781107238428 1299399959 9781299399952 1107336066 9781107336063 |
| language | English |
| oclc_num | 830001169 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (vii, 278 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Cambridge tracts in mathematics ; |
| series2 | Cambridge tracts in mathematics ; |
| spelling | Gurski, Nick, 1980- https://id.oclc.org/worldcat/entity/E39PCjy4j8VXFhHHCTm79QTbkC http://id.loc.gov/authorities/names/n2013005857 Coherence in three-dimensional category theory / Nick Gurski, University of Sheffield. Cambridge : Cambridge University Press, 2013. 1 online resource (vii, 278 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Cambridge tracts in mathematics ; 201 Includes bibliographical references and index. Introduction -- Background: Bicategorical background ; Coherence for bicategories ; Gray-categories -- Tricategories: The algebraic definition of tricategory ; Examples ; Free constructions ; Basic structure ; Gray-categories and tricategories ; Coherence via Yoneda ; Coherence via free constructions -- Gray-monads: Codescent in Gray-categories ; Codescent as a weighted colimit ; Gray-monads and their algebras ; The reflection of lax algebras into strict algebras ; A general coherence result. "Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence theorem, of which this book provides a definitive treatment, as well as covering related results. Along the way the author treats such material as the Gray tensor product and gives a construction of the fundamental 3-groupoid of a space. The book serves as a comprehensive introduction, covering essential material for any student of coherence and assuming only a basic understanding of higher category theory. It is also a reference point for many key concepts in the field and therefore a vital resource for researchers wishing to apply higher categories or coherence results in fields such as algebraic topology or theoretical computer science"-- Provided by publisher "In the study of higher categories, dimension three occupies an interesting position on the landscape of higher dimensional category theory. From the perspective of a "hands-on" approach to defining weak n-categories, tricategories represent the most complicated kind of higher category that the community at large seems comfortable working with."-- Provided by publisher Print version record. English. Tricategories. http://id.loc.gov/authorities/subjects/sh95004189 Tricatégories. MATHEMATICS Logic. bisacsh MATHEMATICS Algebra Linear. bisacsh Categorías (Matemáticas) embne Tricategories fast Electronic book. has work: Coherence in three-dimensional category theory (Text) https://id.oclc.org/worldcat/entity/E39PCGp4m6MVyqPcJppy9CthBK https://id.oclc.org/worldcat/ontology/hasWork Print version: Gurski, Nick, 1980- Coherence in three-dimensional category theory. Cambridge : Cambridge University Press, 2013 9781107034891 (DLC) 2012051079 (OCoLC)813938959 Cambridge tracts in mathematics ; 201. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=539308 Volltext |
| spellingShingle | Gurski, Nick, 1980- Coherence in three-dimensional category theory / Cambridge tracts in mathematics ; Introduction -- Background: Bicategorical background ; Coherence for bicategories ; Gray-categories -- Tricategories: The algebraic definition of tricategory ; Examples ; Free constructions ; Basic structure ; Gray-categories and tricategories ; Coherence via Yoneda ; Coherence via free constructions -- Gray-monads: Codescent in Gray-categories ; Codescent as a weighted colimit ; Gray-monads and their algebras ; The reflection of lax algebras into strict algebras ; A general coherence result. Tricategories. http://id.loc.gov/authorities/subjects/sh95004189 Tricatégories. MATHEMATICS Logic. bisacsh MATHEMATICS Algebra Linear. bisacsh Categorías (Matemáticas) embne Tricategories fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh95004189 |
| title | Coherence in three-dimensional category theory / |
| title_auth | Coherence in three-dimensional category theory / |
| title_exact_search | Coherence in three-dimensional category theory / |
| title_full | Coherence in three-dimensional category theory / Nick Gurski, University of Sheffield. |
| title_fullStr | Coherence in three-dimensional category theory / Nick Gurski, University of Sheffield. |
| title_full_unstemmed | Coherence in three-dimensional category theory / Nick Gurski, University of Sheffield. |
| title_short | Coherence in three-dimensional category theory / |
| title_sort | coherence in three dimensional category theory |
| topic | Tricategories. http://id.loc.gov/authorities/subjects/sh95004189 Tricatégories. MATHEMATICS Logic. bisacsh MATHEMATICS Algebra Linear. bisacsh Categorías (Matemáticas) embne Tricategories fast |
| topic_facet | Tricategories. Tricatégories. MATHEMATICS Logic. MATHEMATICS Algebra Linear. Categorías (Matemáticas) Tricategories Electronic book. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=539308 |
| work_keys_str_mv | AT gurskinick coherenceinthreedimensionalcategorytheory |