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dc.contributor.authorGálvez Carrillo, Maria Immaculada
dc.contributor.authorKock, Joachim
dc.contributor.authorTonks, Andrew
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2019-03-21T16:00:30Z
dc.date.available2019-09-12T00:25:14Z
dc.date.issued2018-09-12
dc.identifier.citationGalvez, M.; Kock, J.; Tonks, A. Decomposition spaces and restriction species. "International mathematics research notices", 12 Setembre 2018, p. 1-44.
dc.identifier.issn1687-0247
dc.identifier.otherhttps://arxiv.org/abs/1708.02570
dc.identifier.urihttp://hdl.handle.net/2117/130730
dc.description.abstractWe show that Schmitt’s restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2-Segal spaces), and that their associated coalgebras are an instance of the general construction of incidence coalgebras of decomposition spaces. We introduce directed restriction species that subsume Schmitt’s restriction species and also induce decomposition spaces. Whereas ordinary restriction species are presheaves on the category of finite sets and injections, directed restriction species are presheaves on the category of finite posets and convex maps. We also introduce the notion of monoidal (directed) restriction species, which induce monoidal decomposition spaces and hence bialgebras, most often Hopf algebras. Examples of this notion include rooted forests, directed graphs, posets, double posets, and many related structures. A prominent instance of a resulting incidence bialgebra is the Butcher–Connes–Kreimer Hopf algebra of rooted trees. Both ordinary and directed restriction species are shown to be examples of a construction of decomposition spaces from certain cocartesian fibrations over the category of finite ordinals that are also cartesian over convex maps. The proofs rely on some beautiful simplicial combinatorics, where the notion of convexity plays a key role. The methods developed are of independent interest as techniques for constructing decomposition spaces
dc.format.extent44 p.
dc.language.isoeng
dc.publisherOxford University Press
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
dc.subject.lcshAlgebraic topology
dc.titleDecomposition spaces and restriction species
dc.typeArticle
dc.subject.lemacTopologia algebraica
dc.contributor.groupUniversitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
dc.identifier.doi10.1093/imrn/rny089
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::18 Category theory; homological algebra::18G Homological algebra
dc.subject.amsClassificació AMS::06 Order, lattices, ordered algebraic structures::06A Ordered sets
dc.subject.amsClassificació AMS::18 Category theory; homological algebra::18G Homological algebra
dc.subject.amsClassificació AMS::55 Algebraic topology::55P Homotopy theory
dc.relation.publisherversionhttps://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rny089/5095270
dc.rights.accessOpen Access
drac.iddocument23940983
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO/6PN/MTM2012-38122-C03-01
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO/1PE/MTM2015-69135-P
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO/1PE/MTM2013-42178-P
dc.relation.projectidinfo:eu-repo/grantAgreement/AGAUR/PRI2010-2013/2014SGR634
dc.relation.projectidinfo:eu-repo/grantAgreement/AGAUR/PRI2017-2019/2017SGR932
dc.relation.projectidinfo:eu-repo/grantAgreement/AEI-FEDER/MTM2016-76453-C2-2-P
upcommons.citation.authorGalvez, M.; Kock, J.; Tonks, A.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameInternational mathematics research notices
upcommons.citation.startingPage1
upcommons.citation.endingPage44


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