The successive dimension, without elegance

Autores
Menni, Matías
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Experience shows that the poset of levels (or dimensions) of the topos of presheaves on some elegant Reedy categories may be equipped with a monotone increasing ‘successor’ function which, as the case of simplicial sets illustrates, is different from Lawvere’s Aufhebung in general. We prove that a similar result holds for the topos of presheaves on a small category with split-epi/mono factorizations; a typical feature of categories that are Reedy elegant, or skeletal, or graphic (von Neumann-)regular, but more general. In fact, we show that the more general ‘successor’ may be described as a function on the poset of full subcategories of the site that are closed under subobjects.
Fil: Menni, Matías. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Universidad Nacional de La Plata. Facultad de Informática. Laboratorio de Investigación y Formación en Informática Avanzada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Materia
Dimension Theory
Topos Theory
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/238395
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The successive dimension, without eleganceMenni, MatíasDimension TheoryTopos Theoryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Experience shows that the poset of levels (or dimensions) of the topos of presheaves on some elegant Reedy categories may be equipped with a monotone increasing ‘successor’ function which, as the case of simplicial sets illustrates, is different from Lawvere’s Aufhebung in general. We prove that a similar result holds for the topos of presheaves on a small category with split-epi/mono factorizations; a typical feature of categories that are Reedy elegant, or skeletal, or graphic (von Neumann-)regular, but more general. In fact, we show that the more general ‘successor’ may be described as a function on the poset of full subcategories of the site that are closed under subobjects.Fil: Menni, Matías. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Universidad Nacional de La Plata. Facultad de Informática. Laboratorio de Investigación y Formación en Informática Avanzada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaAmerican Mathematical Society2024-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/238395Menni, Matías; The successive dimension, without elegance; American Mathematical Society; Proceedings of the American Mathematical Society; 152; 3; 1-2024; 1337-13540002-99391088-6826CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1090/proc/16638info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2024-152-03/S0002-9939-2024-16638-7/home.htmlinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2308.04584v1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T09:48:22Zoai:ri.conicet.gov.ar:11336/238395instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 09:48:23.248CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The successive dimension, without elegance
title The successive dimension, without elegance
spellingShingle The successive dimension, without elegance
Menni, Matías
Dimension Theory
Topos Theory
title_short The successive dimension, without elegance
title_full The successive dimension, without elegance
title_fullStr The successive dimension, without elegance
title_full_unstemmed The successive dimension, without elegance
title_sort The successive dimension, without elegance
dc.creator.none.fl_str_mv Menni, Matías
author Menni, Matías
author_facet Menni, Matías
author_role author
dc.subject.none.fl_str_mv Dimension Theory
Topos Theory
topic Dimension Theory
Topos Theory
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Experience shows that the poset of levels (or dimensions) of the topos of presheaves on some elegant Reedy categories may be equipped with a monotone increasing ‘successor’ function which, as the case of simplicial sets illustrates, is different from Lawvere’s Aufhebung in general. We prove that a similar result holds for the topos of presheaves on a small category with split-epi/mono factorizations; a typical feature of categories that are Reedy elegant, or skeletal, or graphic (von Neumann-)regular, but more general. In fact, we show that the more general ‘successor’ may be described as a function on the poset of full subcategories of the site that are closed under subobjects.
Fil: Menni, Matías. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Universidad Nacional de La Plata. Facultad de Informática. Laboratorio de Investigación y Formación en Informática Avanzada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
description Experience shows that the poset of levels (or dimensions) of the topos of presheaves on some elegant Reedy categories may be equipped with a monotone increasing ‘successor’ function which, as the case of simplicial sets illustrates, is different from Lawvere’s Aufhebung in general. We prove that a similar result holds for the topos of presheaves on a small category with split-epi/mono factorizations; a typical feature of categories that are Reedy elegant, or skeletal, or graphic (von Neumann-)regular, but more general. In fact, we show that the more general ‘successor’ may be described as a function on the poset of full subcategories of the site that are closed under subobjects.
publishDate 2024
dc.date.none.fl_str_mv 2024-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/238395
Menni, Matías; The successive dimension, without elegance; American Mathematical Society; Proceedings of the American Mathematical Society; 152; 3; 1-2024; 1337-1354
0002-9939
1088-6826
CONICET Digital
CONICET
url http://hdl.handle.net/11336/238395
identifier_str_mv Menni, Matías; The successive dimension, without elegance; American Mathematical Society; Proceedings of the American Mathematical Society; 152; 3; 1-2024; 1337-1354
0002-9939
1088-6826
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1090/proc/16638
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2024-152-03/S0002-9939-2024-16638-7/home.html
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2308.04584v1
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.087074

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