A categorical generalization of Klumpenhouwer networks. (English) Zbl 1321.00088

Popoff, Alexandre; Andreatta, Moreno; Ehresmann, Andrée

Collins, Tom (ed.) et al., Mathematics and computation in music. 5th international conference, MCM 2015, London, UK, June 22–25, 2015, Proceedings. Cham: Springer (ISBN 978-3-319-20602-8/pbk; 978-3-319-20603-5/ebook). Lecture Notes in Computer Science 9110. Lecture Notes in Artificial Intelligence, 303-314 (2015).

Summary: This article proposes a functorial framework for generalizing some constructions of transformational theory. We focus on Klumpenhouwer networks for which we propose a categorical generalization via the concept of set-valued poly-K-nets (henceforth PK-nets). After explaining why K-nets are special cases of these category-based transformational networks, we provide several examples of the musical relevance of PK-nets as well as morphisms between them. We also show how to construct new PK-nets by using some topos-theoretical constructions.
For the entire collection see [Zbl 1315.00045].

MSC:

00A65	Mathematics and music
18A30	Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
18B25	Topoi

Keywords:

transformational theory; K-nets; PK-nets; category theory

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