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...

Full description

Bibliographic Details
Main Authors: Forcey, Stefan, Lauve, Aaron, Sottile, Frank
Format: Report
Language:unknown
Published: arXiv 2010
Subjects:
Combinatorics math.CO
Rings and Algebras math.RA
FOS Mathematics
05E, 16
Iceland
Online Access:https://dx.doi.org/10.48550/arxiv.1011.4305
https://arxiv.org/abs/1011.4305
id ftdatacite:10.48550/arxiv.1011.4305
record_format openpolar
spelling 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)
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
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

Similar Items