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2008 Quotients of the multiplihedron as categorified associahedra
Stefan Forcey
Homology Homotopy Appl. 10(2): 227-256 (2008).


We describe a new sequence of polytopes which characterize A∞-maps from a topological monoid to an A∞-space. Therefore each of these polytopes is a quotient of the corresponding multiplihedron. Our sequence of polytopes is demonstrated not to be combinatorially equivalent to the associahedra, as was previously assumed in both topological and categorical literature. They are given the new collective name composihedra. We point out how these polytopes are used to parametrize compositions in the formulation of the theories of enriched bicategories and pseudomonoids in a monoidal bicategory. We also present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the nth polytope in the sequence of composihedra, that is, the nth composihedron $CK(n)$.


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Stefan Forcey. "Quotients of the multiplihedron as categorified associahedra." Homology Homotopy Appl. 10 (2) 227 - 256, 2008.


Published: 2008
First available in Project Euclid: 1 September 2009

zbMATH: 1159.18002
MathSciNet: MR2475611

Primary: 18D20 , 18D50 , 52B12 , 55P43

Keywords: Enriched categories , monoidal categories , n-categories , polytopes

Rights: Copyright © 2008 International Press of Boston

Vol.10 • No. 2 • 2008
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