Homotopy linear algebra

By 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-d...

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Detalles Bibliográficos
Autores: Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437, Kock, Joachim, Tonks, Andrew
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/112830
Acceso en línea:https://hdl.handle.net/2117/112830
https://dx.doi.org/10.1017/S0308210517000208
Access Level:acceso abierto
Palabra clave:Homotopy theory
Algebra, Homological
Algebraic topology
duality
homotopy cardinality
homotopy finiteness
infinity-groupoids
linear algebra
Topologia algebraica
Homotopia, Teoria d'
Àlgebra homològica
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::18 Category theory
homological algebra::18G Homological algebra
Classificació AMS::46 Associative rings and algebras::46A Topological linear spaces and related structures
Classificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
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spelling Homotopy linear algebraGálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437Kock, JoachimTonks, AndrewHomotopy theoryAlgebra, HomologicalAlgebraic topologydualityhomotopy cardinalityhomotopy finitenessinfinity-groupoidslinear algebraTopologia algebraicaHomotopia, Teoria d'Àlgebra homològicaClassificació AMS::55 Algebraic topology::55P Homotopy theoryClassificació AMS::15 Linear and multilinear algebramatrix theoryClassificació AMS::18 Category theoryhomological algebra::18G Homological algebraClassificació AMS::46 Associative rings and algebras::46A Topological linear spaces and related structuresClassificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systemsÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraicaBy 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.Peer Reviewed20182018-04-0120182018-01-16journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/112830https://dx.doi.org/10.1017/S0308210517000208reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1128302026-05-27T15:37:01Z
dc.title.none.fl_str_mv Homotopy linear algebra
title Homotopy linear algebra
spellingShingle Homotopy linear algebra
Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Homotopy theory
Algebra, Homological
Algebraic topology
duality
homotopy cardinality
homotopy finiteness
infinity-groupoids
linear algebra
Topologia algebraica
Homotopia, Teoria d'
Àlgebra homològica
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::18 Category theory
homological algebra::18G Homological algebra
Classificació AMS::46 Associative rings and algebras::46A Topological linear spaces and related structures
Classificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
title_short Homotopy linear algebra
title_full Homotopy linear algebra
title_fullStr Homotopy linear algebra
title_full_unstemmed Homotopy linear algebra
title_sort Homotopy linear algebra
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 Homotopy theory
Algebra, Homological
Algebraic topology
duality
homotopy cardinality
homotopy finiteness
infinity-groupoids
linear algebra
Topologia algebraica
Homotopia, Teoria d'
Àlgebra homològica
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::18 Category theory
homological algebra::18G Homological algebra
Classificació AMS::46 Associative rings and algebras::46A Topological linear spaces and related structures
Classificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
topic Homotopy theory
Algebra, Homological
Algebraic topology
duality
homotopy cardinality
homotopy finiteness
infinity-groupoids
linear algebra
Topologia algebraica
Homotopia, Teoria d'
Àlgebra homològica
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::18 Category theory
homological algebra::18G Homological algebra
Classificació AMS::46 Associative rings and algebras::46A Topological linear spaces and related structures
Classificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
description By 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.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-04-01
2018
2018-01-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/112830
https://dx.doi.org/10.1017/S0308210517000208
url https://hdl.handle.net/2117/112830
https://dx.doi.org/10.1017/S0308210517000208
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
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
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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