Gesture Theory: topos-theoretic perspectives and philosophical framework
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Autores
Arias Valero, Juan Sebastián
Director
Zalamea Traba, Fernando
Tipo de contenido
Trabajo de grado - Doctorado
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EspañolFecha de publicación
2018-04
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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 (Texto tomado de la fuente).