Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-03T19:54:33.043Z Has data issue: false hasContentIssue false
  • English
  • Français

SHEAFIFICATION AS A DESIGN TECHNIQUE FOR CREATIVE PRESERVATION – PRINCIPLES, ILLUSTRATIONS, AND FIRST APPLICATIONS

Published online by Cambridge University Press:  19 June 2023

Pascal Le Masson ,
Armand Hatchuel  and
Benoit Weil
Pascal Le Masson*
Affiliation:
Mines Paris-PSL
Armand Hatchuel
Affiliation:
Mines Paris-PSL
Benoit Weil
Affiliation:
Mines Paris-PSL
*
Le Masson, Pascal, MINES ParisTech-PSL, France, [email protected]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In times of ‘grand challenges’, design theorists dealing with complex systems are facing a dilemma: grand challenges require rule breaking, but they also require the preservation, as much as possible, of existing resources, systems, know-how and societal values. Design for transition calls not for ‘creative destruction’, but for ‘creative preservation’. How do we model a design process that involves ‘creative preservation’?

Today, it is recognized that category/topos theory provides a solid foundation for modelling complex systems and their evolution in design processes. Category theory can account for a design process inside a given ‘theory of the object’, while topos theory and design theory can account for the phenomena whereby a design process is innovative to preserve the knowledge structure. At the heart of this creative preservation is sheafification.

In this study, we analyse the sheafification process using design theory. First, we characterize sheafification from a design perspective. Next, we propose a very simple illustration involving the sheafification of an ordinal 2 category presheaf. Finally, we show how sheafification can be used to enable ‘creative preservation’ in specific complex systems.

Keywords

category theoryInnovationDesign theorycreative preservationKnowledge management
Type
Article
Information
Proceedings of the Design Society , Volume 3: ICED23 , July 2023 , pp. 3165 - 3174
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
The Author(s), 2023. Published by Cambridge University Press

References

Breiner, S, Subrahmanian, E, Jones, A (2017) Categorical foundations for system engineering. In: Madni, AM, Boehm, B, Erwin, DA, Ghanem, R, Wheaton, MJ (eds) 5th Annual Conference on Systems Engineering Research (CSER), 2017.Google Scholar
Cohen, P (1963) The independence of the Continuum Hypothesis. Proceedings of the National Academy of Science 50:1143–1148.CrossRefGoogle ScholarPubMed
Crilly, N (2015) Fixation and creativity in concept development: The attitudes and practices of expert designers. Design Studies 38:54–91.CrossRefGoogle Scholar
Einstein, A (2011) Letters to Solovine (1906–1955).Google Scholar
Giesa, T, Jagadeesan, R, Spivak, DI, Buehler, MJ (2015) Matriarch: A Python Library for Materials Architecture. ACS Biomaterials Science & Engineering 1 (10):1009–1015.CrossRefGoogle ScholarPubMed
Hatchuel, A, Le Masson, P, Weil, B, Carvajal-Perez, D (2019) Innovative Design Within Tradition - Injecting Topos Structures in C-K Theory to Model Culinary Creation Heritage (reviewers'favourite award). Proceedings of the Design Society: International Conference on Engineering Design 1 (1):1543–1552.Google Scholar
Hatchuel, A, Weil, B, Le Masson, P (2013) Towards an ontology of design: lessons from C-K Design theory and Forcing. Research in Engineering Design 24 (2):147–163.CrossRefGoogle Scholar
Kokshagina, O, Le Masson, P, Weil, B (2013) How design theories enable the design of generic technologies: notion of generic concepts and Genericity building operators Paper presented at the International Conference on Engineering Design, ICED'13, Séoul, Korea,Google Scholar
Kostecki, RP (2011) An Introduction to Topos Theory. Institute of Theoretical Physics, WarsawGoogle Scholar
Lawvere, FW (1964) An elementary Theory of the Category of sets. Proceedings of the National Academy of Sciences 52 (6):1506–1511.CrossRefGoogle ScholarPubMed
Le Masson, P, El Qaoumi, K, Hatchuel, A, Weil, B (2019) A Law of Functional Expansion - Eliciting the Dynamics of Consumer Goods Innovation with Design Theory (reviewers'favourite award). Proceedings of the Design Society: International Conference on Engineering Design 1 (1):1015–1024.Google Scholar
Le Masson, P, Hatchuel, A, Kokshagina, O, Weil, B (2016) Designing Techniques for Systemic Impact - Lessons from C-K theory and Matroid Structures. Research in Engineering Design 28 (3):275–298.CrossRefGoogle Scholar
Mac Lane, S, Moerdijk, I (1992) Sheaves in Geometry and Logic. A First Introduction to Topos Theory. Universitext. Springer, New YorkGoogle Scholar
McMahon, CA, Eckert, CM, Fadel, G (2021) Towards a Debate on the Positioning of Engineering Design. Proceedings of the Design Society 1 (160011.png): 3169–3178.CrossRefGoogle Scholar
Prouté, A (2007) Sur quelques liens entre théorie des topos et théorie de la démonstration. Paper presented at the Conférence faite à l'Université de la Méditerrannée le 29 mai 2007.Google Scholar
Prouté, A (2016) Introduction à la logique catégorique. CNRS / Univesrité Paris Didrerot, ParisGoogle Scholar
Rosiak, D (2022) Sheaf Theory Through Examples. MIT Press, Boston, MACrossRefGoogle Scholar
Schumpeter, JA (1939) Business Cycles: A Theoretical, Historical and Statistical Analysis of the Capitalist Process. first abridged edition 1964, first edition 1939 edn. McGraw Hill Book Company, New York and LondonGoogle Scholar
Short, R, Hylton, A, Cleveland, J, Moy, M, Cardona, R, Green, R, Curry, J, Mallery, B, Bainbridge, G, Memon, Z (2022) Sheaf Theoretic Models for Routing in Delay Tolerant Networks. In: 2022 IEEE Aerospace Conference (AERO), 5–12 March 2022 2022. pp 1–19. https://dx.doi.org/10.1109/AERO53065.2022.9843504CrossRefGoogle Scholar
Spivak, DI (2013) Category Theory for Scientists.Google Scholar
Tierney, M (1972) Sheaf theory and the continuum hypothesis. In: Lawvere, FW (ed) Toposes, algebraic geometry and logic. Springer Verlag, Heidelberg, pp 13–42CrossRefGoogle Scholar
Ullah, AS (2020) What is knowledge in Industry 4.0? Engineering Reports n/a (n/a):e12217.CrossRefGoogle Scholar