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(2015) Mathematics and computation in music, Dordrecht, Springer.
A categorical generalization of Klumpenhouwer networks
Alexandre Popoff, Andrée C. Ehresmann , Moreno Andreatta
pp. 303-314
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.
Publication details
DOI: 10.1007/978-3-319-20603-5_31
Full citation:
Popoff, A. , Ehresmann, A. C. , Andreatta, M. (2015)., A categorical generalization of Klumpenhouwer networks, in T. Collins, D. Meredith & A. Volk (eds.), Mathematics and computation in music, Dordrecht, Springer, pp. 303-314.