Atribución-NoComercial 4.0 InternacionalZalamea Traba, FernandoArias Valero, Juan Sebastián2019-07-022019-07-022018-04https://repositorio.unal.edu.co/handle/unal/63339Using 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 (Texto tomado de la fuente).application/pdfspaDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/1 Filosofía y psicología / Philosophy and psychology510 Matemáticas / Mathematics780 Música / MusicTrabajo de grado - Doctoradohttp://bdigital.unal.edu.co/63632/info:eu-repo/semantics/openAccessGesture theoryMathematical music theoryMathematical philosophyTopos theorySimplicial setsSemi-simplicial setsKan extensionsWeighted limits