Gesture Theory: topos-theoretic perspectives and philosophical framework

Abstract: Using tools from category theory and 2-category theory, in particular from topos theory, we present the rudiments of a theory of mathematical gestures and hypergestures, including diverse incarnations thereof: topological gestures, gestures on locales, gestures on topological categories, g...

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Autores:
Arias Valero, Juan Sebastián
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2018
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/63339
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/63339
http://bdigital.unal.edu.co/63632/
Palabra clave:
1 Filosofía y psicología / Philosophy and psychology
51 Matemáticas / Mathematics
78 Música / Music
Gesture theory
Mathematical music theory
Mathematical philosophy
Topos theory
Simplicial sets
Semi-simplicial sets
Kan extensions
Weighted limits
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_285e00a178ccdebf071f57ef8e252b50
oai_identifier_str oai:repositorio.unal.edu.co:unal/63339
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Zalamea Traba, FernandoArias Valero, Juan Sebastiánd2966df1-ae1b-465e-8117-aa4597a6f8d33002019-07-02T21:41:43Z2019-07-02T21:41:43Z2018-04https://repositorio.unal.edu.co/handle/unal/63339http://bdigital.unal.edu.co/63632/Abstract: Using tools from category theory and 2-category theory, in particular from topos theory, we present the rudiments of a theory of mathematical gestures and hypergestures, including diverse incarnations thereof: topological gestures, gestures on locales, gestures on topological categories, gestures in elementary topoi, diagrams in categories, Mazzola's formulas, and gestures on Grothendieck topoi. In particular, we address the problem of the exponential presentation of certain objects of gestures and hypergestures in some of these instances, for example, in the representative cases of gestures on topological spaces and diagrams in categories. After the mathematical work, we present a philosophical and methodological reflection on gesture theory, mainly based on Galois, Riemann, Kan, Grothendieck, Peirce, Merleau-Ponty, Zalamea, and Mazzola.Doctoradoapplication/pdfspaUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Matemáticas MatemáticasMatemáticasArias Valero, Juan Sebastián (2018) Gesture Theory: topos-theoretic perspectives and philosophical framework. Doctorado thesis, Universidad Nacional de Colombia - Sede Bogotá.1 Filosofía y psicología / Philosophy and psychology51 Matemáticas / Mathematics78 Música / MusicGesture theoryMathematical music theoryMathematical philosophyTopos theorySimplicial setsSemi-simplicial setsKan extensionsWeighted limitsGesture Theory: topos-theoretic perspectives and philosophical frameworkTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDORIGINALThesisfinal.pdfapplication/pdf2009750https://repositorio.unal.edu.co/bitstream/unal/63339/1/Thesisfinal.pdfdda45d0843a77e96dbffb2b36e602e7aMD51THUMBNAILThesisfinal.pdf.jpgThesisfinal.pdf.jpgGenerated Thumbnailimage/jpeg4303https://repositorio.unal.edu.co/bitstream/unal/63339/2/Thesisfinal.pdf.jpgfbabf24ce1184349974f567f8067acb5MD52unal/63339oai:repositorio.unal.edu.co:unal/633392024-04-28 23:11:14.162Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Gesture Theory: topos-theoretic perspectives and philosophical framework
title Gesture Theory: topos-theoretic perspectives and philosophical framework
spellingShingle Gesture Theory: topos-theoretic perspectives and philosophical framework
1 Filosofía y psicología / Philosophy and psychology
51 Matemáticas / Mathematics
78 Música / Music
Gesture theory
Mathematical music theory
Mathematical philosophy
Topos theory
Simplicial sets
Semi-simplicial sets
Kan extensions
Weighted limits
title_short Gesture Theory: topos-theoretic perspectives and philosophical framework
title_full Gesture Theory: topos-theoretic perspectives and philosophical framework
title_fullStr Gesture Theory: topos-theoretic perspectives and philosophical framework
title_full_unstemmed Gesture Theory: topos-theoretic perspectives and philosophical framework
title_sort Gesture Theory: topos-theoretic perspectives and philosophical framework
dc.creator.fl_str_mv Arias Valero, Juan Sebastián
dc.contributor.author.spa.fl_str_mv Arias Valero, Juan Sebastián
dc.contributor.spa.fl_str_mv Zalamea Traba, Fernando
dc.subject.ddc.spa.fl_str_mv 1 Filosofía y psicología / Philosophy and psychology
51 Matemáticas / Mathematics
78 Música / Music
topic 1 Filosofía y psicología / Philosophy and psychology
51 Matemáticas / Mathematics
78 Música / Music
Gesture theory
Mathematical music theory
Mathematical philosophy
Topos theory
Simplicial sets
Semi-simplicial sets
Kan extensions
Weighted limits
dc.subject.proposal.spa.fl_str_mv Gesture theory
Mathematical music theory
Mathematical philosophy
Topos theory
Simplicial sets
Semi-simplicial sets
Kan extensions
Weighted limits
description Abstract: Using tools from category theory and 2-category theory, in particular from topos theory, we present the rudiments of a theory of mathematical gestures and hypergestures, including diverse incarnations thereof: topological gestures, gestures on locales, gestures on topological categories, gestures in elementary topoi, diagrams in categories, Mazzola's formulas, and gestures on Grothendieck topoi. In particular, we address the problem of the exponential presentation of certain objects of gestures and hypergestures in some of these instances, for example, in the representative cases of gestures on topological spaces and diagrams in categories. After the mathematical work, we present a philosophical and methodological reflection on gesture theory, mainly based on Galois, Riemann, Kan, Grothendieck, Peirce, Merleau-Ponty, Zalamea, and Mazzola.
publishDate 2018
dc.date.issued.spa.fl_str_mv 2018-04
dc.date.accessioned.spa.fl_str_mv 2019-07-02T21:41:43Z
dc.date.available.spa.fl_str_mv 2019-07-02T21:41:43Z
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
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dc.type.content.spa.fl_str_mv Text
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status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/63339
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/63632/
url https://repositorio.unal.edu.co/handle/unal/63339
http://bdigital.unal.edu.co/63632/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Matemáticas Matemáticas
Matemáticas
dc.relation.references.spa.fl_str_mv Arias Valero, Juan Sebastián (2018) Gesture Theory: topos-theoretic perspectives and philosophical framework. Doctorado thesis, Universidad Nacional de Colombia - Sede Bogotá.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/63339/1/Thesisfinal.pdf
https://repositorio.unal.edu.co/bitstream/unal/63339/2/Thesisfinal.pdf.jpg
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