Sheafification as a design technique for creative preservation - principles, illustrations, and first applications

DS 122: Proceedings of the Design Society: 24th International Conference on Engineering Design (ICED23)

Year: 2023
Editor: Kevin Otto, Boris Eisenbart, Claudia Eckert, Benoit Eynard, Dieter Krause, Josef Oehmen, Nad
Author: Le Masson, Pascal; Hatchuel, Armand; Weil, Benoit
Series: ICED
Institution: Mines Paris-PSL
Section: Design Methods
Page(s): 3165-3174
DOI number:


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 theory, Innovation, Design theory, creative preservation, Knowledge management

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