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Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
dc.contributor.author | Gálvez Carrillo, Maria Immaculada |
dc.contributor.author | Kock, Joachim |
dc.contributor.author | Tonks, Andrew |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-03-10T09:18:11Z |
dc.date.available | 2016-03-10T09:18:11Z |
dc.date.issued | 2015-12 |
dc.identifier.citation | Galvez, M., Kock, J., Tonks, A. "Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals". 2015. |
dc.identifier.uri | http://hdl.handle.net/2117/84104 |
dc.description.abstract | 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 |
dc.format.extent | 34 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica |
dc.subject.lcsh | Algebraic topology |
dc.subject.lcsh | Combinatorial topology |
dc.subject.other | Algebraic Topology |
dc.subject.other | Combinatorics |
dc.title | Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals |
dc.type | External research report |
dc.subject.lemac | Topologia algebraica |
dc.subject.lemac | Topologia combinatòria |
dc.contributor.group | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
dc.subject.ams | Classificació AMS::18 Category theory; homological algebra::18G Homological algebra |
dc.subject.ams | Classificació AMS::06 Order, lattices, ordered algebraic structures::06A Ordered sets |
dc.subject.ams | Classificació AMS::55 Algebraic topology::55P Homotopy theory |
dc.relation.publisherversion | http://arxiv.org/abs/1512.07580 |
dc.rights.access | Open Access |
local.identifier.drac | 17543218 |
dc.description.version | Preprint |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2012-38122-C03-01/ES/GEOMATRIA ALGEBRAICA, SIMPLECTICA, ARITMETICA Y APLICACIONES/ |
dc.relation.projectid | info:eu-repo/grantAgreement/AGAUR/PRI2010-2013/2014SGR634 |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2015-69135-P/ES/GEOMETRIA Y TOPOLOGIA DE VARIEDADES, ALGEBRA Y APLICACIONES/ |
local.citation.author | Galvez, M.; Kock, J.; Tonks, A. |
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