Skip to main content

Gestures on Locales and Localic Topoi

  • Chapter
  • First Online:
The Musical-Mathematical Mind

Part of the book series: Computational Music Science ((CMS))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The statements made in this section must be interpreted in a suitable 2-categorical sense.

References

  1. Escardó, M.H., Heckmann, R.: Topologies on spaces of continuous functions. In: Topology Proceedings, vol. 26, edn. 2, pp. 545–564 (2001–2002)

    Google Scholar 

  2. Hyland, J.M.E.: Function Spaces in the Category of Locales, Lecture Notes in Mathematics, vol. 871, pp 264–281. Springer, Berlin (1981)

    Google Scholar 

  3. Johnstone, P.T.: Stone Spaces, Cambridge Studies in Advanced Mathematics, vol. 3. Cambridge University Press, Cambridge (1982)

    Google Scholar 

  4. 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)

    Google Scholar 

  5. Johnstone, P.T.: Sketches of an Elephant: A Topos Theory Compendium. vol. 2. Oxford University Press, Oxford (2002)

    Google Scholar 

  6. Mac Lane, S., Moerdijk, I.: Sheaves in Geometry and Logic. Springer, Berlin (1992)

    Google Scholar 

  7. Mazzola, G., et al.: The Topos of Music: Geometric Logic of Concepts, Theory, and Performance. Birkhäuser, Basel et al (2002)

    Book  MATH  Google Scholar 

  8. Mazzola, G., Andreatta, M.: Diagrams, gestures and formulae in music. J. Math. Music 1(1), 23–46 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Mazzola, G.: Categorical gestures, the diamond conjecture, lewin’s question, and the hammerklavier sonata. J. Math. Music 3(1), 31–58 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Moerdijk, I., Wraith, G.: Connected locally connected toposes are path connected. Trans. Am. Math. Soc. 295, 849–859 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  11. 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)

    Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Juan Sebastián Arias .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Arias, J.S. (2017). Gestures on Locales and Localic Topoi. In: Pareyon, G., Pina-Romero, S., Agustín-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

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-47337-6_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47336-9

  • Online ISBN: 978-3-319-47337-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics