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RT Book, Whole SR Electronic DC OPAC T1 Functorial Semiotics for Creativity in Music and Mathematics / by Guerino Mazzola, Sangeeta Dey, Zilu Chen, Yan Pang T2 Computational Music Science. ISSN:18680313 A1 Mazzola, Guerino A1 Dey, Sangeeta A1 Chen, Zilu A1 Pang, Yan A1 SpringerLink (Online service) YR 2022 FD 2022 SP XIII, 166 p K1 Music -- Mathematics K1 Semiotics K1 Computational neuroscience K1 Art -- Study and teaching K1 Artificial intelligence K1 Mathematics -- Data processing K1 Mathematics in Music K1 Semiotics K1 Computational Neuroscience K1 Creativity and Arts Education K1 Artificial Intelligence K1 Computational Mathematics and Numerical Analysis ED 1st ed. 2022. PB Springer International Publishing : Imprint: Springer PP Cham SN 9783030851903 LA English (英語) CL LCC:T57-57.97 CL LCC:ML1-3930 CL DC23:780.0519 NO Part I Orientation -- Part II General Concepts -- Part III Semantic Math -- Part IV Applications -- Part V Conclusions -- References -- Index NO 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 Čech 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 NO HTTP:URL=https://doi.org/10.1007/978-3-030-85190-3 NO 書誌ID=EB00002260; LK [E Book]https://doi.org/10.1007/978-3-030-85190-3 OL 30