Higher categories, strings, cubes and simplex equations

Ross Street

doi:10.1007/BF00872948

Higher categories, strings, cubes and simplex equations

Ross Street^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

Abstract

This survey of categorical structures, occurring naturally in mathematics, physics and computer science, deals with monoidal categories; various structures in monoidal categories; free monoidal structures; Penrose string notation; 2-dimensional categorical structures; the simplex equations of field theory and statistical mechanics; higher-order categories and computads; the (v,d)-cube equations; the simplex equations as cubical cocycle equations; and, cubes, braids and higher braids.

Original language	English
Pages (from-to)	29-77
Number of pages	49
Journal	Applied Categorical Structures
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/BF00872948
Publication status	Published - Mar 1995

Keywords

bicategory
braiding
cocycle
cubes
d-simplex equation
higher braids
Mathematics Subject Classifications (1991): 18D00, 82B23, 52B11
Monoidal category
n-category
pasting
string notation
tangles
tensor category

Access to Document

10.1007/BF00872948

Cite this

@article{7ae0dc4922ae497da70ae518986e8f8d,

title = "Higher categories, strings, cubes and simplex equations",

abstract = "This survey of categorical structures, occurring naturally in mathematics, physics and computer science, deals with monoidal categories; various structures in monoidal categories; free monoidal structures; Penrose string notation; 2-dimensional categorical structures; the simplex equations of field theory and statistical mechanics; higher-order categories and computads; the (v,d)-cube equations; the simplex equations as cubical cocycle equations; and, cubes, braids and higher braids.",

keywords = "bicategory, braiding, cocycle, cubes, d-simplex equation, higher braids, Mathematics Subject Classifications (1991): 18D00, 82B23, 52B11, Monoidal category, n-category, pasting, string notation, tangles, tensor category",

author = "Ross Street",

year = "1995",

month = mar,

doi = "10.1007/BF00872948",

language = "English",

volume = "3",

pages = "29--77",

journal = "Applied Categorical Structures",

issn = "0927-2852",

publisher = "Springer, Springer Nature",

number = "1",

}

TY - JOUR

T1 - Higher categories, strings, cubes and simplex equations

AU - Street, Ross

PY - 1995/3

Y1 - 1995/3

N2 - This survey of categorical structures, occurring naturally in mathematics, physics and computer science, deals with monoidal categories; various structures in monoidal categories; free monoidal structures; Penrose string notation; 2-dimensional categorical structures; the simplex equations of field theory and statistical mechanics; higher-order categories and computads; the (v,d)-cube equations; the simplex equations as cubical cocycle equations; and, cubes, braids and higher braids.

AB - This survey of categorical structures, occurring naturally in mathematics, physics and computer science, deals with monoidal categories; various structures in monoidal categories; free monoidal structures; Penrose string notation; 2-dimensional categorical structures; the simplex equations of field theory and statistical mechanics; higher-order categories and computads; the (v,d)-cube equations; the simplex equations as cubical cocycle equations; and, cubes, braids and higher braids.

KW - bicategory

KW - braiding

KW - cocycle

KW - cubes

KW - d-simplex equation

KW - higher braids

KW - Mathematics Subject Classifications (1991): 18D00, 82B23, 52B11

KW - Monoidal category

KW - n-category

KW - pasting

KW - string notation

KW - tangles

KW - tensor category

UR - http://www.scopus.com/inward/record.url?scp=0003187995&partnerID=8YFLogxK

U2 - 10.1007/BF00872948

DO - 10.1007/BF00872948

M3 - Article

AN - SCOPUS:0003187995

VL - 3

SP - 29

EP - 77

JO - Applied Categorical Structures

JF - Applied Categorical Structures

SN - 0927-2852

IS - 1

ER -

Higher categories, strings, cubes and simplex equations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this