Functorial semiotics for creativity

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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.

Original languageEnglish (US)
Pages (from-to)66-105
Number of pages40
JournalJournal of Mathematics and Music
Issue number1
StatePublished - Jan 2 2020

Bibliographical note

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.


  • Hjelmslev extensions
  • Yoneda lemma
  • computational creativity
  • denotators
  • forms
  • functors
  • music semiotics


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