Functorial semiotics for creativity. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Mazzola, Guerino
• Is Part Of: Journal of mathematics and music. Volume 14:Issue 1(2020)
• Page Start: 66
• Page End: 105
• Publication Date: 2020-01-02
• Subjects: music semiotics -- Hjelmslev extensions -- functors -- Yoneda lemma -- computational creativity -- denotators -- forms; 16E30 -- 18A25; Music theory -- Periodicals; Music -- Mathematical models -- Periodicals; Music -- Mathematics -- Periodicals; 781.2
• DOI: 10.1080/17459737.2019.1675193
• Languages: English
• ISSNs: 1745-9737

Abstract

Abstract : 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.