Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'

Autores
Menni, Matías
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let E be a topos. If l is a level of E with monic skeleta then it makes sense to consider the objects in E that have l-skeletal boundaries. In particular, if p : E o S is a pre-cohesive geometric morphism then its centre (that may be called level 0) has monic skeleta. Let level 1 be the Aufhebung of level 0. We show that if level 1 has monic skeleta then the quotients of 0-separated objects with 0-skeletal boundaries are 1-skeletal. We also prove that in several examples (such as the classifier of non-trivial Boolean algebras, simplicial sets and the classifier of strictly bipointed objects) every 1-skeletal object is of that form.
Fil: Menni, Matías. 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
Topos Theory
Axiomatic Cohesion
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:11336/128722
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'Menni, MatíasTopos TheoryAxiomatic Cohesionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let E be a topos. If l is a level of E with monic skeleta then it makes sense to consider the objects in E that have l-skeletal boundaries. In particular, if p : E o S is a pre-cohesive geometric morphism then its centre (that may be called level 0) has monic skeleta. Let level 1 be the Aufhebung of level 0. We show that if level 1 has monic skeleta then the quotients of 0-separated objects with 0-skeletal boundaries are 1-skeletal. We also prove that in several examples (such as the classifier of non-trivial Boolean algebras, simplicial sets and the classifier of strictly bipointed objects) every 1-skeletal object is of that form.Fil: Menni, Matías. 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; ArgentinaRobert Rosebrugh2019-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/128722Menni, Matías; Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'; Robert Rosebrugh; Theory And Applications Of Categories; 34; 25; 9-2019; 714-7351201-561XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/34/25/34-25abs.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:23:54Zoai:ri.conicet.gov.ar:11336/128722instacron: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:34982025-09-10 13:23:54.431CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'
title Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'
spellingShingle Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'
Menni, Matías
Topos Theory
Axiomatic Cohesion
title_short Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'
title_full Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'
title_fullStr Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'
title_full_unstemmed Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'
title_sort Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'
dc.creator.none.fl_str_mv Menni, Matías
author Menni, Matías
author_facet Menni, Matías
author_role author
dc.subject.none.fl_str_mv Topos Theory
Axiomatic Cohesion
topic Topos Theory
Axiomatic Cohesion
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let E be a topos. If l is a level of E with monic skeleta then it makes sense to consider the objects in E that have l-skeletal boundaries. In particular, if p : E o S is a pre-cohesive geometric morphism then its centre (that may be called level 0) has monic skeleta. Let level 1 be the Aufhebung of level 0. We show that if level 1 has monic skeleta then the quotients of 0-separated objects with 0-skeletal boundaries are 1-skeletal. We also prove that in several examples (such as the classifier of non-trivial Boolean algebras, simplicial sets and the classifier of strictly bipointed objects) every 1-skeletal object is of that form.
Fil: Menni, Matías. 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 Let E be a topos. If l is a level of E with monic skeleta then it makes sense to consider the objects in E that have l-skeletal boundaries. In particular, if p : E o S is a pre-cohesive geometric morphism then its centre (that may be called level 0) has monic skeleta. Let level 1 be the Aufhebung of level 0. We show that if level 1 has monic skeleta then the quotients of 0-separated objects with 0-skeletal boundaries are 1-skeletal. We also prove that in several examples (such as the classifier of non-trivial Boolean algebras, simplicial sets and the classifier of strictly bipointed objects) every 1-skeletal object is of that form.
publishDate 2019
dc.date.none.fl_str_mv 2019-09
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/11336/128722
Menni, Matías; Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'; Robert Rosebrugh; Theory And Applications Of Categories; 34; 25; 9-2019; 714-735
1201-561X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/128722
identifier_str_mv Menni, Matías; Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'; Robert Rosebrugh; Theory And Applications Of Categories; 34; 25; 9-2019; 714-735
1201-561X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/34/25/34-25abs.html
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
dc.publisher.none.fl_str_mv Robert Rosebrugh
publisher.none.fl_str_mv Robert Rosebrugh
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
_version_ 1842981322694328320
score 12.48226

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