Gesture Theory: topos-theoretic perspectives and philosophical framework

• Autores: Juan Sebastián Arias Valero
• Directores de la Tesis: Fernando Zalamea Traba (dir. tes.)
• Lectura: En la Universidad Nacional de Colombia (UNAL) ( Colombia ) en 2018
• Idioma: español
• Materias:
  • Ciencias de las artes y las letras
    • Teoría análisis y critica literarias
    • Teoría análisis y critica de las bellas artes
    • Otras especialidades artísticas
• Enlaces
  • Tesis en acceso abierto en: repositorio.unal.edu.co
• Resumen

  • 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.