Innovative Design Within Tradition - Injecting Topos Structures in C-K Theory to Model Culinary Creation Heritage

In "Grande cuisine" creation and tradition co-evolve in a rich number of ways. Great chefs still use recipes from the 19th century and may also reinvent gastronomy itself. The creation heritage of culinary Art is the paradoxical capacity to both "respect" tradition and "break" its rules. Building on C-K theory, we show that such creative heritage needs multiple and independent layers of knowledge that "speak" of basic fixed objects. These properties correspond to general mathematical structures that we find in Topos theory. Thus, C-K/Topos predicts creative design strategies that can respect tradition in different ways. It also proves a form of "innovation within tradition"-"sheafification" in Topos words-that is not a compromise and builds on tradition itself. These findings fit with the lessons of great books of gastronomy. C-K/Topos has a wide scope of validity: it applies to any innovative design that needs preserving systemic structures, like engineering systems or social and environmental systems. C-K/Topos models with a high generality how local and radical innovation can warrant systems incremental change. C-K/Topos will have implications for teaching and research.