The permutoassociahedron, Mac Lane’s coherence theorem and asymptotic zones for the KZ equation. (English) Zbl 0812.18003

Kapranov, Mikhail M.

J. Pure Appl. Algebra 85, No. 2, 119-142 (1993).

All possible bracketings of \(n\) symbols in all possible orders are exhibited as vertices of a combinatorial CW-complex \(KP_ n\). It is clearly relevant to the coherence of symmetric monoidal categories, yet also fits nicely into Drinfel’d’s study of the Knizhnik-Zamolodchikov equations and into the analysis of the Grothendieck-Knudsen moduli space of stable \(n\)-pointed curves of genus 0.

Reviewer: R.H.Street (North Ryde)

MSC:

18D10	Monoidal, symmetric monoidal and braided categories (MSC2010)
14D10	Arithmetic ground fields (finite, local, global) and families or fibrations
35Q99	Partial differential equations of mathematical physics and other areas of application
19D23	Symmetric monoidal categories

Keywords:

associahedron; braided tensor category; coherence; symmetric monoidal categories; Knizhnik-Zamolodchikov equations; Grothendieck-Knudsen moduli space

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