References
- Agustín-Aquino, Octavio A., Julien Junod, and Guerino Mazzola. 2015. Computational Counterpoint Worlds: Mathematical Theory, Software, and Experiments. Cham, Switzerland: Springer International Publishing.
- Arias, Juan S. 2017a. “Abstract Gestures: A Unifying Concept in Mathematical Music Theory.” In Mathematics and Computation in Music, edited by Octavio A. Agustín-Aquino, Emilio Lluis-Puebla, and Mariana Montiel, 183–200. Cham, Switzerland: Springer International Publishing.
- Arias, Juan S. 2017b. “Gestures on Locales and Localic Topoi.” In The Musical-Mathematical Mind: Patterns and Transformations, edited by Gabriel Pareyon, Silvia Pina-Romero, Octavio A. Agustín-Aquino, and Emilio Lluis-Puebla, 29–39. Cham, Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-319-47337-6_4.
- Arias, Juan S. 2018. “Gesture Theory: Topos-Theoretic Perspectives and Philosophical Framework.” PhD thesis, Universidad Nacional de Colombia. http://bdigital.unal.edu.co/63632/1/Thesisfinal.pdf.
- Cadoz, Claude, and Marcelo M. Wanderley. 2000. “Gesture-Music.” In Trends in Gestural Control of Music, edited by Marcelo Wanderley and Marc Battier. Ircam – Centre Pompidou. https://hal.archives-ouvertes.fr/hal-01105543.
- de Saint-Victor, Hugues. 1854. “De Institutione Novitiorum.” In Patrologia Latina, Tomus CLXXVI, Hugonis de S. Victore … opera omnia, Vol. 2 edited by Jacques-Paul Migne, Cols. 925–952. Paris: Jacques-Paul Migne.
- Day, B. J., and Kelly, G. M. 1970. “On topological quotient maps preserved by pullbacks or products.” Proc. Cambridge Philos. Soc. 67 (3): 553–558.
- Ehresmann, Andrée C., and Jean-Paul Vanbremeersch. 2007. Memory Evolutive Systems: Hierarchy, Emergence, Cognition. Amsterdam, The Netherlands: Elsevier Science.
- Escardó, Martín, and Reinhold Heckmann. 2001–02. “Topologies on Spaces of Continuous Functions.” Topology Proceedings 26 (2): 545–564. http://topology.auburn.edu/tp/reprints/v26/tp26209.pdf.
- Fiore, Thomas M., and Thomas Noll. 2011. “Commuting Groups and the Topos of Triads.” In Mathematics and Computation in Music, edited by Carlos Agon, Moreno Andreatta, Gérard Assayag, Emmanuel Amiot, Jean Bresson, and John Mandereau, 69–83. Vol. 6726 of Lecture Notes in Computer Science. Berlin: Springer. https://doi.org/10.1007/978-3-642-21590-2_6.
- Fox, Ralph H. 1945. “On topologies for function spaces.” Bulletin of the American Mathematical Society 51 (6): 429–432. doi: 10.1090/S0002-9904-1945-08370-0
- Fritsch, Rudolf, and Renzo Piccinini. 1990. Cellular Structures in Topology. Vol. 19 in the series Cambridge Studies in Advanced Mathematics. Cambridge, UK: Cambridge University Press.
- Fritsch, Rudolf, and Renzo A. Piccinini. 1993. “CW-complexes and Euclidean Spaces.” Rendiconti del Circolo Matematico di Palermo 2 (24): 79–95. https://epub.ub.uni-muenchen.de/4524/index.html.
- Godøy, Rolf I., and Marc Leman, eds. 2010. Musical Gestures: Sound, Movement, and Meaning. New York: Routledge. https://www.routledge.com/Musical-Gestures-Sound-Movement-and-Meaning/Godoy-Leman/p/book/9780415998871.
- Johnstone, Peter T. 1982. Stone Spaces. Cambridge, UK: Cambridge University Press.
- Lurie, Jacob. 2009. Higher Topos Theory. Princeton, NJ: Princeton University Press.
- Mac Lane, Saunders. 1998. Categories for the Working Mathematician. New York: Springer-Verlag.
- Mac Lane, Saunders, and Ieke Moerdijk. 1992. Sheaves in Geometry and Logic: A First Introduction to Topos Theory. Universitext. New York: Springer Science.
- Mannone, Maria. 2018. “Knots, Music and DNA.” Journal of Creative Music Systems 2 (2). http://jcms.org.uk/issues/Vol2Issue2/knots-music-and-dna/article.html.
- Mazzola, Guerino. 2009. “Categorical Gestures, the Diamond Conjecture, Lewin’s Question, and the Hammerklavier Sonata.” Journal of Mathematics and Music 3 (1): 31–58. https://doi.org/10.1080/17459730902910480.
- Mazzola, Guerino. 2012. “Singular Homology on Hypergestures.” Journal of Mathematics and Music 6 (1): 49–60. https://doi.org/10.1080/17459737.2012.680311.
- Mazzola, Guerino, and Moreno Andreatta. 2006. “From a Categorical Point of View: K-nets as Limit Denotators.” Perspectives of New Music 44 (1): 88–113.
- Mazzola, Guerino, and Moreno Andreatta. 2007. “Diagrams, Gestures and Formulae in Music.” Journal of Mathematics and Music 1 (1): 23–46. http://doi.org/10.1080/17459730601137716.
- Mazzola, G., Paul B. Cherlin, Mathias Rissi, and Nathan Kennedy. 2008. Flow, Gesture, and Spaces in Free Jazz: Towards a Theory of Collaboration. Berlin: Springer.
- Mazzola, Guerino, René Guitart, Jocelyn Ho, Alex Lubet, Maria Mannone, Matt Rahaim, and Florian Thalmann. 2017. The Topos of Music III: Gestures. Musical Multiverse Ontologies. Cham, Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-319-64481-3.
- Mazzola, Guerino, and Maria Mannone. 2016. “Global Functorial Hypergestures over General Skeleta for Musical Performance.” Journal of Mathematics and Music 10 (3): 227–243. https://doi.org/10.1080/17459737.2016.1195456.
- Mazzola, Guerino, et al. 2017. The Topos of Music. 2nd ed. 4 vols. Cham, Switzerland: Springer International Publishing.
- Milnor, John. 1957. “The Geometric Realization of a Semi-Simplicial Complex.” Annals of Mathematics 65 (2): 357–362. doi: 10.2307/1969967
- Müller, Stefan. 2004. “Pianist’s Hands: Synthesis of Musical Gestures.” PhD thesis, University of Zürich.
- Noll, Thomas. 2005. “The Topos of Triads.” In Proceedings of the Colloquium on Mathematical Music Theory, edited by Harald Fripertinger and Ludwig Reich, 103–135. Graz, Austria: Karl-Franzens-Universität.
- Phillips, Steven, and William H. Wilson. 2016. “Systematicity and a Categorical Theory of Cognitive Architecture: Universal Construction in Context.” Frontiers in Psychology 7: 2–14. https://www.frontiersin.org/article/10.3389/fpsyg.2016.01139.
- Popoff, Alexandre, Moreno Andreatta, and Andrée Ehresmann. 2015. “A Categorical Generalization of Klumpenhouwer Networks.” In Mathematics and Computation in Music, edited by Tom Collins, David Meredith, and Anja Volk, 303–314. Cham, Switzerland: Springer International Publishing.
- Spivak, David I. 2014. Category Theory for the Sciences. Cambridge, MA: MIT Press.
- Steenrod, N. E. 1967. “A convenient category of topological spaces.” The Michigan Mathematical Journal 14 (2): 133–152. doi: 10.1307/mmj/1028999711
- Zalamea, Fernando. 2017. “Mazzola, Galois, Peirce, Riemann, and Merleau-Ponty: A Triadic, Spatial Framework for Gesture Theory.” In The Musical-Mathematical Mind: Patterns and Transformations, edited by Gabriel Pareyon, Silvia Pina-Romero, Octavio A. Agustín-Aquino, and Emilio Lluis-Puebla, 339–345. Cham, Switzerland: Springer International Publishing. doi: 10.1007/978-3-319-47337-6_33