Higher categories, strings, cubes and simplex equations

Ross Street*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    23 Citations (Scopus)


    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 languageEnglish
    Pages (from-to)29-77
    Number of pages49
    JournalApplied Categorical Structures
    Issue number1
    Publication statusPublished - Mar 1995


    • 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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