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Homotopy linear algebra

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.accessioned2018-01-16T09:24:19Z
dc.date.available2018-04-17T00:30:39Z
dc.date.issued2018-04
dc.identifier.citationGalvez, M., Kock, J., Tonks, A. Homotopy linear algebra. "Proceedings of the Royal Society of Edinburgh: Section A Mathematics", Abril 2018, Volume 148, Issue 2, p. 293-325
dc.identifier.issn1473-7124
dc.identifier.urihttp://hdl.handle.net/2117/112830
dc.description.abstractBy homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into 8-categories to model the duality between vector spaces and profinite-dimensional vector spaces, and set up a global notion of homotopy cardinality à la Baez, Hoffnung and Walker compatible with this duality. We needed these results to support our work on incidence algebras and Möbius inversion over 8-groupoids; we hope that they can also be of independent interest.
dc.format.extent1 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
dc.subject.lcshHomotopy theory
dc.subject.lcshAlgebra, Homological
dc.subject.lcshAlgebraic topology
dc.subject.otherduality
dc.subject.otherhomotopy cardinality
dc.subject.otherhomotopy finiteness
dc.subject.otherinfinity-groupoids
dc.subject.otherlinear algebra
dc.titleHomotopy linear algebra
dc.typeArticle
dc.subject.lemacTopologia algebraica
dc.subject.lemacHomotopia, Teoria d'
dc.subject.lemacÀlgebra homològica
dc.contributor.groupUniversitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
dc.identifier.doi10.1017/S0308210517000208
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::55 Algebraic topology::55P Homotopy theory
dc.subject.amsClassificació AMS::15 Linear and multilinear algebra; matrix theory
dc.subject.amsClassificació AMS::18 Category theory; homological algebra::18G Homological algebra
dc.subject.amsClassificació AMS::46 Associative rings and algebras::46A Topological linear spaces and related structures
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systems
dc.relation.publisherversionhttps://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/homotopy-linear-algebra/8E584127A7FB28AE5520B6604C7FC3C2
dc.rights.accessOpen Access
local.identifier.drac21623747
dc.description.versionPostprint (author's final draft)
local.citation.authorGalvez, M.; Kock, J.; Tonks, A.
local.citation.publicationNameProceedings of the Royal Society of Edinburgh: Section A Mathematics
local.citation.startingPage1
local.citation.endingPage1


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