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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/238392
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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 Técnicas2025-10-15T15:46:01Zoai: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:34982025-10-15 15:46:01.473CONICET 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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13.22299 |