Cofree compositions of coalgebras (extended abstract)

Autor:	Forcey, Stefan, Lauve, Aaron, Sottile, Frank
Rok vydání:	2010
Předmět:	Mathematics - Combinatorics Mathematics - Rings and Algebras 05E 16
Druh dokumentu:	Working Paper
Popis:	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. Comment: 13 pages, 67 .eps figures. Extended abstract for Formal Power Series and Algebraic Combinatorics, Reykjavik, Iceland June 2011
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1011.4305 Zobrazit plný text záznamu View this record from Arxiv