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.