This book presents a new semiotic theory based upon category theory and applying to a classification of creativity in music and mathematics. It is the first functorial approach to mathematical semiotics that can be applied to AI implementations for creativity by using topos theory and its applications to music theory.

Of particular interest is the generalized Yoneda embedding in the bidual of the category of categories (Lawvere) - parametrizing semiotic units - enabling a ech cohomology of manifolds of semiotic entities. It opens up a conceptual mathematics as initiated by Grothendieck and Galois and allows a precise description of musical and mathematical creativity, including a classification thereof in three types. This approach is new, as it connects topos theory, semiotics, creativity theory, and AI objectives for a missing link to HI (Human Intelligence).

The reader can apply creativity research using our classification, cohomology theory, generalized Yoneda embedding, and Java implementation of the presented functorial display of semiotics, especially generalizing the Hjelmslev architecture. The intended audience are academic, industrial, and artistic researchers in creativity.

The first functorial semiotic theory for creativity in music and mathematics Application of topos theory to the classification of creativity Proposes object-oriented schemes for software implementation of AI of creativity

Autorentext

Prof. Dr. Guerino Mazzola earned his Ph.D. in Mathematics from Zurich University. He wrote the groundbreaking book The Topos of Music in 2002, its formal language and models are used by leading researchers in Europe, India, Japan, and North America and have become a foundation of music software design. Prof. Mazzola has an appointment as professor in the School of Music at the College of Liberal Arts, University of Minnesota. Maria Mannone and Yan Pang are completing their Ph.D. work in the School of Music of the University of Minnesota. Margaret O'Brien and Nathan Torunsky are undergraduate students in the School of Music of the University of Minnesota.

Inhalt
Part I Orientation.- Part II General Concepts.- Part III Semantic Math.- Part IV Applications.- Part V Conclusions.- References.- Index.