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

25 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

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10.1007/BF00872948

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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

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Higher categories, strings, cubes and simplex equations

Abstract

Keywords

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