Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals

Decomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors between decomposition spaces induce coalgebra homomorphisms. Suitable added finiteness conditions define the notion of Mö...

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Detalhes bibliográficos
Autores: Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437, Kock, Joachim, Tonks, Andrew
Formato: informe técnico
Fecha de publicación:2015
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/84104
Acesso em linha:https://hdl.handle.net/2117/84104
Access Level:acceso abierto
Palavra-chave:Algebraic topology
Combinatorial topology
Algebraic Topology
Combinatorics
Topologia algebraica
Topologia combinatòria
Classificació AMS::18 Category theory
homological algebra::18G Homological algebra
Classificació AMS::06 Order, lattices, ordered algebraic structures::06A Ordered sets
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
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spelling Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervalsGálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437Kock, JoachimTonks, AndrewAlgebraic topologyCombinatorial topologyAlgebraic TopologyCombinatoricsTopologia algebraicaTopologia combinatòriaClassificació AMS::18 Category theoryhomological algebra::18G Homological algebraClassificació AMS::06 Order, lattices, ordered algebraic structures::06A Ordered setsClassificació AMS::55 Algebraic topology::55P Homotopy theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraicaDecomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors between decomposition spaces induce coalgebra homomorphisms. Suitable added finiteness conditions define the notion of Möbius decomposition space, a far-reaching generalisation of the notion of Möbius category of Leroux. In this paper, we show that the Lawvere-Menni Hopf algebra of Möbius intervals, which contains the universal Möbius function (but is not induced by a Möbius category), can be realised as the homotopy cardinality of a Möbius decomposition space U of all Möbius intervals, and that in a certain sense U is universal20152015-12-0120162016-03-10reporthttp://purl.org/coar/resource_type/c_93fcAOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/reportapplication/pdfapplication/pdfhttps://hdl.handle.net/2117/84104reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengMinisterio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2012-38122-C03-01 GEOMATRIA ALGEBRAICA, SIMPLECTICA, ARITMETICA Y APLICACIONESMinisterio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2015-69135-P GEOMETRIA Y TOPOLOGIA DE VARIEDADES, ALGEBRA Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/841042026-05-27T15:37:01Z
dc.title.none.fl_str_mv Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
title Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
spellingShingle Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Algebraic topology
Combinatorial topology
Algebraic Topology
Combinatorics
Topologia algebraica
Topologia combinatòria
Classificació AMS::18 Category theory
homological algebra::18G Homological algebra
Classificació AMS::06 Order, lattices, ordered algebraic structures::06A Ordered sets
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
title_short Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
title_full Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
title_fullStr Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
title_full_unstemmed Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
title_sort Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
dc.creator.none.fl_str_mv Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Kock, Joachim
Tonks, Andrew
author Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
author_facet Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Kock, Joachim
Tonks, Andrew
author_role author
author2 Kock, Joachim
Tonks, Andrew
author2_role author
author
dc.subject.none.fl_str_mv Algebraic topology
Combinatorial topology
Algebraic Topology
Combinatorics
Topologia algebraica
Topologia combinatòria
Classificació AMS::18 Category theory
homological algebra::18G Homological algebra
Classificació AMS::06 Order, lattices, ordered algebraic structures::06A Ordered sets
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
topic Algebraic topology
Combinatorial topology
Algebraic Topology
Combinatorics
Topologia algebraica
Topologia combinatòria
Classificació AMS::18 Category theory
homological algebra::18G Homological algebra
Classificació AMS::06 Order, lattices, ordered algebraic structures::06A Ordered sets
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
description Decomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors between decomposition spaces induce coalgebra homomorphisms. Suitable added finiteness conditions define the notion of Möbius decomposition space, a far-reaching generalisation of the notion of Möbius category of Leroux. In this paper, we show that the Lawvere-Menni Hopf algebra of Möbius intervals, which contains the universal Möbius function (but is not induced by a Möbius category), can be realised as the homotopy cardinality of a Möbius decomposition space U of all Möbius intervals, and that in a certain sense U is universal
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-12-01
2016
2016-03-10
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/84104
url https://hdl.handle.net/2117/84104
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2012-38122-C03-01 GEOMATRIA ALGEBRAICA, SIMPLECTICA, ARITMETICA Y APLICACIONES
Ministerio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2015-69135-P GEOMETRIA Y TOPOLOGIA DE VARIEDADES, ALGEBRA Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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