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.
Das ist wohl schon die Mathematik des “Neuen Zeitalters”.
Alexander Grothendieck [397] on “Geometrie der Töne” [682]
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Mazzola, G. (2017). Topoi of Music. In: The Topos of Music I: Theory. Computational Music Science. Springer, Cham. https://doi.org/10.1007/978-3-319-64364-9_19
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DOI: https://doi.org/10.1007/978-3-319-64364-9_19
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