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This paper presents a conceptual mathematical framework for developing rich human–machine interactions in order to improve decision-making in a social organisation, S. The idea is to model how S can create a “multi-level artificial cognitive system”, called a data analyser (DA), to collaborate with humans in collecting and learning how to analyse data, to anticipate situations, and to develop new responses, thus improving decision-making. In this model, the DA is “processed” to not only gather data and extend existing knowledge, but also to learn how to act autonomously with its own specific procedures or even to create new ones. An application is given in cases where such rich human–machine interactions are expected to allow the DA+S partnership to acquire deep anticipation capabilities for possible future changes, e.g., to prevent risks or seize opportunities. The way the social organization S operates over time, including the construction of DA, is described using the conceptual framework comprising “memory evolutive systems” (MES), a mathematical theoretical approach introduced by Ehresmann and Vanbremeersch for evolutionary multi-scale, multi-agent and multi-temporality systems. This leads to the definition of a “data analyser–MES”.

Cet article s’intéresse à l’apport de la théorie mathématique des catégories pour appréhender les processus d’invention collective. En particulier, il s’agit de présenter et de discuter une approche « catégorielle » fondée sur les systèmes évolutifs à mémoire (MES). Les MES ont été introduits dans les années quatre-vingt dix (Ehresmann et Vanbremeersch, 1991) dans le but d’analyser des systèmes complexes évolutifs intégrant une hétérogénéité de composants, d’échelles et de temporalités (Ehresmann and Vanbremeersch 2007). Conçus pour synthétiser les caractéristiques communes à des systèmes biologiques, cognitifs ou sociaux, ils ont eu des applications variées en biologie ou en traitement de l'information, mais leur principale application a été l'étude du développement des processus cognitifs d'ordre supérieur, incluant les processus de créativité et d’anticipation (modèle « MENS »). Cet article approfondit la construction d’un MES particulier, nommé D-MES (Béjean et Ehresmann, 2015), pour appréhender les processus d’invention collective.

Domain-independent design theories grounded on formal frameworks are of interest for a wide spectrum ofprofessional and academic fields, including design education, design management and innovation strategy. While muchattention has been paid to the modeling of the specification process of an artifact, less attention has been paid to themodeling of the creative social interactions involved in the process of designing. There is still a need for conceptualapproaches that could further integrate the creative,collective, cognitive and emotional aspects of design. This paperaims to develop such an integrative view by relying on the Memory Evolutive Systems (MES;A. C. Ehresmann andVanbremeersch 2007). Based on a conceptual mathematical domain named "Category Theory",MES provide arelational approach for studying evolutionary, multi-scale, multi-temporality and self-organized systems. Using the MESapproach, we develop a conceptual framework which encompasses the various phases of a design process and considershow it is directed by the multiple mental and social interactions between different actors. Our approach, named D-MES,extends prior research by providing a formal account of how various entities can operate in parallel to develop creativecombinations of new shared objects and processes of different levels of complexity throughout the design process. Anillustration is provided in the case of garden design.

International audience; Domain-independent design theories grounded on formal frameworks are of interest for a wide spectrum of professional and academic fields, including design education, design management and innovation strategy. While much attention has been paid to the modeling of the specification process of an artifact, less attention has been paid to the modeling of the creative social interactions involved in the process of designing. There is still a need for conceptual approaches that could further integrate the creative, collective, cognitive and emotional aspects of design. This paper aims to develop such an integrative view by relying on the Memory Evolutive Systems (MES) (A. C. Ehresmann and Vanbremeersch 2007). Based on a conceptual mathematical domain named “Category Theory,” MES provide a relational approach for studying evolutionary, multi-scale, multi-temporality and self-organized systems. Using the MES approach, we develop a conceptual framework which encompasses the various phases of a design process and considers how it is directed by the multiple mental and social interactions between different actors. Our approach, named D-MES, extends prior research by providing a formal account of how various entities can operate in parallel to develop creative combinations of new shared objects and processes of different levels of complexity throughout the design process. An illustration is provided in the case of garden design.

The problem of characterizing colimits in graphs (i.e., in free categories) has arisen in connection with the modelisation of natural systems such as biological or neural systems. Indeed, in a series of papers with J.-P. Vanbremeersch since 1986, we have developed a model based on category theory, where the emergence of complex objects is modelled by a completion process. The present results show that this process cannot be done in the sole framework of graphs, since they imply that the completion of a free category is not free. This vindicates our recourse to (general) categories, instead of considering only graphs as some people have advocated., http://www.numdam.org/item/DIA_1997__37__3_0/