Higher categories, strings, cubes and simplex equations (Q1346409)

This is a survey of some categorical structures, notably monoidal categories, and higher dimensional ramifications hereof, which have recently proved to be of interest in the theory of quantum groups, knot theory, and statistical mechanics. The author himself, and his collaborators, have been among the prime initiators of this fascinating application of category theory, and the article provides a good introduction to and bibliography for it. It also provides some new viewpoints on the Yang-Baxter and Zamolodchikov equations, in terms of (non-abelian) cohomology with coefficients in higher dimensional categories.