Bi-directional models of 'radically synthetic' differential geometry

Autores
Menni, Matías
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The radically synthetic foundation for smooth geometry formulated in [Law11] postulates a space T with the property that it has a unique point and, out of the monoid T^T of endomorphisms, it extracts a submonoid R which, in many cases, is the (commutative) multiplication of a rig structure. The rig R is said to be bi-directional if its subobject of invertible elements has two connected components. In this case, R may be equipped with a pre-order compatible with the rig structure.We adjust the construction of `well-adapted´ models of Synthetic Differential Geometry in order to build the first pre-cohesive toposes with a bi-directional R.We also show that, in one of these pre-cohesive variants, the pre-order on R, derived radically synthetically from bi-directionality, coincides with that defined in the original model.
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
Synthetic Differential Geometry
Axiomatic Cohesion
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:11336/238392
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/238392
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Bi-directional models of 'radically synthetic' differential geometryMenni, MatíasSynthetic Differential GeometryAxiomatic CohesionTopos Theoryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The radically synthetic foundation for smooth geometry formulated in [Law11] postulates a space T with the property that it has a unique point and, out of the monoid T^T of endomorphisms, it extracts a submonoid R which, in many cases, is the (commutative) multiplication of a rig structure. The rig R is said to be bi-directional if its subobject of invertible elements has two connected components. In this case, R may be equipped with a pre-order compatible with the rig structure.We adjust the construction of `well-adapted´ models of Synthetic Differential Geometry in order to build the first pre-cohesive toposes with a bi-directional R.We also show that, in one of these pre-cohesive variants, the pre-order on R, derived radically synthetically from bi-directionality, coincides with that defined in the original model.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; ArgentinaMount Allison University2024-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/238392Menni, Matías; Bi-directional models of 'radically synthetic' differential geometry; Mount Allison University; Theory And Applications Of Categories; 40; 15; 5-2024; 413-4291201-561XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2405.17748info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2405.17748info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:54:04Zoai:ri.conicet.gov.ar:11336/238392instacron: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 10:54:04.871CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Bi-directional models of 'radically synthetic' differential geometry
title Bi-directional models of 'radically synthetic' differential geometry
spellingShingle Bi-directional models of 'radically synthetic' differential geometry
Menni, Matías
Synthetic Differential Geometry
Axiomatic Cohesion
Topos Theory
title_short Bi-directional models of 'radically synthetic' differential geometry
title_full Bi-directional models of 'radically synthetic' differential geometry
title_fullStr Bi-directional models of 'radically synthetic' differential geometry
title_full_unstemmed Bi-directional models of 'radically synthetic' differential geometry
title_sort Bi-directional models of 'radically synthetic' differential geometry
dc.creator.none.fl_str_mv Menni, Matías
author Menni, Matías
author_facet Menni, Matías
author_role author
dc.subject.none.fl_str_mv Synthetic Differential Geometry
Axiomatic Cohesion
Topos Theory
topic Synthetic Differential Geometry
Axiomatic Cohesion
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 The radically synthetic foundation for smooth geometry formulated in [Law11] postulates a space T with the property that it has a unique point and, out of the monoid T^T of endomorphisms, it extracts a submonoid R which, in many cases, is the (commutative) multiplication of a rig structure. The rig R is said to be bi-directional if its subobject of invertible elements has two connected components. In this case, R may be equipped with a pre-order compatible with the rig structure.We adjust the construction of `well-adapted´ models of Synthetic Differential Geometry in order to build the first pre-cohesive toposes with a bi-directional R.We also show that, in one of these pre-cohesive variants, the pre-order on R, derived radically synthetically from bi-directionality, coincides with that defined in the original model.
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 The radically synthetic foundation for smooth geometry formulated in [Law11] postulates a space T with the property that it has a unique point and, out of the monoid T^T of endomorphisms, it extracts a submonoid R which, in many cases, is the (commutative) multiplication of a rig structure. The rig R is said to be bi-directional if its subobject of invertible elements has two connected components. In this case, R may be equipped with a pre-order compatible with the rig structure.We adjust the construction of `well-adapted´ models of Synthetic Differential Geometry in order to build the first pre-cohesive toposes with a bi-directional R.We also show that, in one of these pre-cohesive variants, the pre-order on R, derived radically synthetically from bi-directionality, coincides with that defined in the original model.
publishDate 2024
dc.date.none.fl_str_mv 2024-05
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/11336/238392
Menni, Matías; Bi-directional models of 'radically synthetic' differential geometry; Mount Allison University; Theory And Applications Of Categories; 40; 15; 5-2024; 413-429
1201-561X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/238392
identifier_str_mv Menni, Matías; Bi-directional models of 'radically synthetic' differential geometry; Mount Allison University; Theory And Applications Of Categories; 40; 15; 5-2024; 413-429
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/arxiv/https://arxiv.org/abs/2405.17748
info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2405.17748
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 Mount Allison University
publisher.none.fl_str_mv Mount Allison University
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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