Why tricategories?

*(English)*Zbl 0829.18003This paper may be seen as a “trailer” for the author’s recently- published monograph with R. Gordon and R. Street [“Coherence for tricategories”, Mem. Am. Math. Soc. 558 (1995)], aimed particularly at that part of the theoretical computer science community which has learned to appreciate the importance of category theory for the foundations of computer science. The author shows how higher-dimensional categories (in particular tricategories) arise naturally in computer science, and how the coherence problems which arise from such structures become of practical relevance. He also sketches how these coherence problems are tackled in the Gordon-Power-Street monograph; for detailed proofs the reader is referred to the latter.

Reviewer: P.T.Johnstone (Cambridge)