Higher categories, strings, cubes and simplex equations
type: Item
instance of: scholarly article
title: Higher categories, strings, cubes and simplex equations
zbMATH Open document ID: 0827.18002
DOI: 10.1007/BF00872948
published in: Applied Categorical Structures
publication date: 1995-04-04T00:00:00Z
review text: This is a survey of some categorical structures, notably monoidal categories, and higher dimensional ramifications hereof, which have recently proved to be of interest in the theory of quantum groups, knot theory, and statistical mechanics. The author himself, and his collaborators, have been among the prime initiators of this fascinating application of category theory, and the article provides a good introduction to and bibliography for it. It also provides some new viewpoints on the Yang-Baxter and Zamolodchikov equations, in terms of (non-abelian) cohomology with coefficients in higher dimensional categories.
reviewed by: Anders Kock
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 82B23
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 18-02
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 18G50
zbMATH DE Number: 740363
zbMATH Keywords: string notation
zbMATH Keywords: braiding
zbMATH Keywords: cocycle
zbMATH Keywords: Yang-Baxter equations
zbMATH Keywords: non-abelian cohomology
zbMATH Keywords: survey
zbMATH Keywords: monoidal categories
zbMATH Keywords: quantum groups
zbMATH Keywords: knot theory
zbMATH Keywords: statistical mechanics
zbMATH Keywords: bibliography
zbMATH Keywords: Zamolodchikov equations
Wikidata QID: Q56687265
author: Ross H. Street
MaRDI profile type: Publication
cites work: Cartesian bicategories. I
cites work: On formulations and solutions of simplex equations.
cites work: Braided compact closed categories with applications to low dimensional topology
cites work: Coherence theorems via knot theory
cites work: Simplex equations and their solutions
cites work: Coherence for tricategories
cites work: Homotopical algebra in homotopical categories
cites work: Formal category theory: Adjointness for 2-categories
cites work: Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems
cites work: Tortile Yang-Baxter operators in tensor categories
cites work: The geometry of tensor calculus. I
cites work: Q3978992
cites work: Braided tensor categories
cites work: On MacLane's conditions for coherence of natural associativities, commutativities, etc
cites work: Generators and relations for \(\Delta\) as a monoidal 2-category
cites work: Q3972992
cites work: From Petri nets to linear logic
cites work: Classical and quantum conformal field theory
cites work: Q3324593
cites work: A 2-categorical pasting theorem
cites work: Modeling concurrency with partial orders
cites work: Ribbon graphs and their invariants derived from quantum groups
cites work: Tortile tensor categories
cites work: Homotopy Associativity of H-Spaces. I
cites work: The algebra of directed complexes
cites work: Q5665322
cites work: Limits indexed by category-valued 2-functors
cites work: The algebra of oriented simplexes
cites work: Q3994019
cites work: The Yang-Baxter equation and invariants of links
Recommended article: Erratum to: Higher categories, strings, cubes and simplex equations
Recommended article: SOME CATEGORICAL ASPECTS OF SIMPLICIAL COMPLEXES
Recommended article: String diagrams and categorification
Recommended article: Higher dimensional obstruction theory in algebraic categories
Recommended article: Categorification and Higher Representation Theory
Recommended article: Q3159161
Recommended article: Higher Categories and Homotopical Algebra
Recommended article: Q5872357
Recommended article: Q4397217
Recommended article: Cubical and simplicial sets in the category of quivers
description: scientific article; zbMATH DE number 740363