Quotients of the Multiplihedron as Categorified Associahedra

Details Quotients of the Multiplihedron as Categorified Associahedra Quotients of the Multiplihedron as Categorified Associahedra

2008-03-18

arxiv.org/abs/0803.2694v4

Mathematics

Category Theory

29 pages, for more pictures see http://faculty.tnstate.edu/sforcey References updated, details of a new realization of associa

Scientific paper

We describe a new sequence of polytopes which characterize A_infinity maps from a topological monoid to an A_infinity space. Therefore each of these polytopes is a quotient of the corresponding multiplihedron. Later term(s) in our sequence of polytopes are demonstrated not to be combinatorially equivalent to the associahedron, as was previously assumed. They are given the new collective name composihedra. We point out how these polytopes are used to parameterize compositions in the formulation of the theories of enriched bicategories and pseudomonoids in a monoidal bicategory. We 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.

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