| 书目名称 | Functorial Semiotics for Creativity in Music and Mathematics |
| 编辑 | Guerino Mazzola,Sangeeta Dey,Yan Pang |
| 视频video | |
| 概述 | 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 implementatio |
| 丛书名称 | Computational Music Science |
| 图书封面 |  |
| 描述 | .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 crea |
| 出版日期 | Book 2022 |
| 关键词 | semiotics; creativity; music; mathematics; cohomology; categories; functors; Yoneda Lemma; topos; Grothendiec |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-85190-3 |
| isbn_softcover | 978-3-030-85192-7 |
| isbn_ebook | 978-3-030-85190-3Series ISSN 1868-0305 Series E-ISSN 1868-0313 |
| issn_series | 1868-0305 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 18:42:47
