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Higher categories, strings, cubes and simplex equations

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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.

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  1. Mathematics Department, Macquarie University, 2109, NSW, Australia

    Ross Street

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Street, R. Higher categories, strings, cubes and simplex equations. Appl Categor Struct 3, 29–77 (1995). https://doi.org/10.1007/BF00872948

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