Abstract
We present a motivation and a proposal for the definition of gestures and hypergestures on locales and localic topoi. Further possible generalizations, including gestures on Grothendieck topoi are discussed.
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Notes
- 1.
The statements made in this section must be interpreted in a suitable 2-categorical sense.
References
Escardó, M.H., Heckmann, R.: Topologies on spaces of continuous functions. In: Topology Proceedings, vol. 26, edn. 2, pp. 545–564 (2001–2002)
Hyland, J.M.E.: Function Spaces in the Category of Locales, Lecture Notes in Mathematics, vol. 871, pp 264–281. Springer, Berlin (1981)
Johnstone, P.T.: Stone Spaces, Cambridge Studies in Advanced Mathematics, vol. 3. Cambridge University Press, Cambridge (1982)
Johnstone, P.T.: The Art of Pointless Thinking: A Student’s Guide to the Category of Locale. In: Herrlich, H., Porst, H.-E. (eds.) Category Theory at Work, pp. 85–107. Heldermann, Berlin (1991)
Johnstone, P.T.: Sketches of an Elephant: A Topos Theory Compendium. vol. 2. Oxford University Press, Oxford (2002)
Mac Lane, S., Moerdijk, I.: Sheaves in Geometry and Logic. Springer, Berlin (1992)
Mazzola, G., et al.: The Topos of Music: Geometric Logic of Concepts, Theory, and Performance. Birkhäuser, Basel et al (2002)
Mazzola, G., Andreatta, M.: Diagrams, gestures and formulae in music. J. Math. Music 1(1), 23–46 (2007)
Mazzola, G.: Categorical gestures, the diamond conjecture, lewin’s question, and the hammerklavier sonata. J. Math. Music 3(1), 31–58 (2009)
Moerdijk, I., Wraith, G.: Connected locally connected toposes are path connected. Trans. Am. Math. Soc. 295, 849–859 (1986)
Pedicchio, M.C., Tholen, W. (eds.): Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory, Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2004)
Acknowledgements
I sincerely thank Professors Fernando Zalamea and Guerino Mazzola for allowing me to work in MaMuTh under their guidance, offering me their confidence and marvellous insights in mathematics, art, and philosophy.
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Arias, J.S. (2017). Gestures on Locales and Localic Topoi. In: Pareyon, G., Pina-Romero, S., AgustÃn-Aquino, O., Lluis-Puebla, E. (eds) The Musical-Mathematical Mind. Computational Music Science. Springer, Cham. https://doi.org/10.1007/978-3-319-47337-6_4
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DOI: https://doi.org/10.1007/978-3-319-47337-6_4
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