Topoi of Music

  • Guerino Mazzola
Chapter
Part of the Computational Music Science book series (CMS)

Summary

This chapter is a conceptual synthesis of the previous achievements. We show that the overall structure of the category Glob of global compositions carries a Grothendieck pretopology via finite covering families. It is well known that such a pretopology generates a Grothendieck topology J and therefore a Lawvere{Tierny topology j on the presheaf topos Glob@. We discuss the associated instances, such as the subobject classifier sheaf Ω, and the subtopos Sh(J; Glob) of sheaves.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Guerino Mazzola
    • 1
  1. 1.School of MusicUniversity of MinnesotaMinneapolisUSA

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