Applied Categorical Structures

, Volume 3, Issue 1, pp 29–77 | Cite as

Higher categories, strings, cubes and simplex equations

  • Ross Street


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.

Mathematics Subject Classifications (1991)

18D00 82B23 52B11 

Key words

Monoidal category tensor category n-category bicategory string notation d-simplex equation braiding tangles cubes cocycle higher braids pasting 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Ross Street
    • 1
  1. 1.Mathematics DepartmentMacquarie UniversityAustralia

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