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, 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.

• 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