Functorial semiotics for creativity. (English) Zbl 1466.00017
Summary: In this paper, we develop a mathematically conceived semiotic theory. This project seems essential for a future computational creativity science since the outcome of the process of creativity must add new signs to given semiotic contexts. The mathematical framework is built upon categories of functors, in particular linearized categories deduced from path categories of digraphs and the Gabriel-Zisman calculus of fractions. Semantics in this approach is extended to a number of “global” constructions enabled by the Yoneda Lemma, including cohomological constructions. This approach concludes with a short discussion of classes of creativity with respect to the proposed functorial semiotics.
MSC:
| 00A65 | Mathematics and music |
| 16E30 | Homological functors on modules (Tor, Ext, etc.) in associative algebras |
| 18A25 | Functor categories, comma categories |
Keywords:
music semiotics; Hjelmslev extensions; functors; Yoneda lemma; computational creativity; denotatorsReferences:
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