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. Along...
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: | BSB01 FHN01 UBR01 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 |
| Beschreibung: | 1 Online-Ressource (vii, 278 Seiten) |
| ISBN: | 9781139542333 |
| DOI: | 10.1017/CBO9781139542333 |
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| 505 | 8 | |a 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 | |
| 520 | |a 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 | ||
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| author | Gurski, Nick 1980- |
| author_GND | (DE-588)1034065572 |
| author_facet | Gurski, Nick 1980- |
| author_role | aut |
| author_sort | Gurski, Nick 1980- |
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| bvnumber | BV043942017 |
| classification_rvk | SK 320 |
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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 |
| ctrlnum | (ZDB-20-CBO)CR9781139542333 (OCoLC)847038522 (DE-599)BVBBV043942017 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139542333 |
| format | Electronic eBook |
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| id | DE-604.BV043942017 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781139542333 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350987 |
| oclc_num | 847038522 |
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| physical | 1 Online-Ressource (vii, 278 Seiten) |
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| publishDate | 2013 |
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| publisher | Cambridge University Press |
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| spelling | Gurski, Nick 1980- Verfasser (DE-588)1034065572 aut Coherence in three-dimensional category theory Nick Gurski, University of Sheffield Cambridge Cambridge University Press 2013 1 Online-Ressource (vii, 278 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 201 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 Tricategories Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-107-03489-1 https://doi.org/10.1017/CBO9781139542333 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Gurski, Nick 1980- Coherence in three-dimensional category theory 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 Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4120552-2 |
| 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 Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Tricategories Kategorientheorie |
| url | https://doi.org/10.1017/CBO9781139542333 |
| work_keys_str_mv | AT gurskinick coherenceinthreedimensionalcategorytheory |