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

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/84104

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
dc.contributor.author	Gálvez Carrillo, Maria Immaculada
dc.contributor.author	Kock, Joachim
dc.contributor.author	Tonks, Andrew
dc.date	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.language.iso	eng
dc.relation	http://arxiv.org/abs/1512.07580
dc.relation	info:eu-repo/grantAgreement/ES/6PN/MTM2012-38122-C03-01
dc.relation	info:eu-repo/grantAgreement/AGAUR/PRI2010-2013/2014SGR634
dc.relation	info:eu-repo/grantAgreement/ES/1PE/MTM2015-69135-P
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
dc.subject	Algebraic topology
dc.subject	Combinatorial topology
dc.subject	Algebraic Topology
dc.subject	Combinatorics
dc.subject	Topologia algebraica
dc.subject	Topologia combinatòria
dc.subject	Classificació AMS::18 Category theory; homological algebra::18G Homological algebra
dc.subject	Classificació AMS::06 Order, lattices, ordered algebraic structures::06A Ordered sets
dc.subject	Classificació AMS::55 Algebraic topology::55P Homotopy theory
dc.title	Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
dc.type	info:eu-repo/semantics/draft
dc.type	info:eu-repo/semantics/report
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

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