Cofree compositions of coalgebras (extended abstract)

Details Cofree compositions of coalgebras (extended abstract) Cofree compositions of coalgebras (extended abstract)

2010-11-18

arxiv.org/abs/1011.4305v2

Mathematics

Combinatorics

13 pages, 67 .eps figures. Extended abstract for Formal Power Series and Algebraic Combinatorics, Reykjavik, Iceland June 2011

Scientific paper

We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and the theory of species. We prove that the composition of two cofree coalgebras is cofree and give conditions which imply that the composition is a one-sided Hopf algebra. These conditions hold when one coalgebra is a graded Hopf operad D and the other is a connected graded coalgebra with coalgebra map to D. We conclude by discussing these structures for compositions with bases the vertices of multiplihedra, composihedra, and hypercubes.

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