Cofree compositions of coalgebras (extended abstract)
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...
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ftdatacite:10.48550/arxiv.1011.4305 2023-05-15T16:48:39+02:00 Cofree compositions of coalgebras (extended abstract) Forcey, Stefan Lauve, Aaron Sottile, Frank 2010 https://dx.doi.org/10.48550/arxiv.1011.4305 https://arxiv.org/abs/1011.4305 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Combinatorics math.CO Rings and Algebras math.RA FOS Mathematics 05E, 16 Preprint Article article CreativeWork 2010 ftdatacite https://doi.org/10.48550/arxiv.1011.4305 2022-04-01T14:29:17Z 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. : 13 pages, 67 .eps figures. Extended abstract for Formal Power Series and Algebraic Combinatorics, Reykjavik, Iceland June 2011 Report Iceland DataCite Metadata Store (German National Library of Science and Technology) |
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ftdatacite |
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topic |
Combinatorics math.CO Rings and Algebras math.RA FOS Mathematics 05E, 16 |
spellingShingle |
Combinatorics math.CO Rings and Algebras math.RA FOS Mathematics 05E, 16 Forcey, Stefan Lauve, Aaron Sottile, Frank Cofree compositions of coalgebras (extended abstract) |
topic_facet |
Combinatorics math.CO Rings and Algebras math.RA FOS Mathematics 05E, 16 |
description |
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. : 13 pages, 67 .eps figures. Extended abstract for Formal Power Series and Algebraic Combinatorics, Reykjavik, Iceland June 2011 |
format |
Report |
author |
Forcey, Stefan Lauve, Aaron Sottile, Frank |
author_facet |
Forcey, Stefan Lauve, Aaron Sottile, Frank |
author_sort |
Forcey, Stefan |
title |
Cofree compositions of coalgebras (extended abstract) |
title_short |
Cofree compositions of coalgebras (extended abstract) |
title_full |
Cofree compositions of coalgebras (extended abstract) |
title_fullStr |
Cofree compositions of coalgebras (extended abstract) |
title_full_unstemmed |
Cofree compositions of coalgebras (extended abstract) |
title_sort |
cofree compositions of coalgebras (extended abstract) |
publisher |
arXiv |
publishDate |
2010 |
url |
https://dx.doi.org/10.48550/arxiv.1011.4305 https://arxiv.org/abs/1011.4305 |
genre |
Iceland |
genre_facet |
Iceland |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1011.4305 |
_version_ |
1766038742133374976 |