Stefan Forcey ; Aaron Lauve ; Frank Sottile

Cofree compositions of coalgebras
dmtcs:2917 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2011,
DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)

https://doi.org/10.46298/dmtcs.2917
Cofree compositions of coalgebras
Authors: Stefan Forcey ^{1}; Aaron Lauve ^{2}; Frank Sottile ^{2}
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Stefan Forcey;Aaron Lauve;Frank Sottile
1 Department of Theoretical and Applied Mathematics
2 Department of Mathematics [Austin]
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 onesided Hopf algebra. These conditions hold when one coalgebra is a graded Hopf operad $\mathcal{D}$ and the other is a connected graded coalgebra with coalgebra map to $\mathcal{D}$. We conclude with examples of these structures, where the factor coalgebras have bases indexed by the vertices of multiplihedra, composihedra, and hypercubes.
Duality between QuasiSymmetrical Functions and the Solomon Descent Algebra
1 Document citing this article
Source : OpenCitations
Forcey, Stefan, 2012, Extending The Tamari Lattice To Some Compositions Of Species, Associahedra, Tamari Lattices And Related Structures, pp. 187210, 10.1007/9783034804059_10.