Colimits in free categories
Andrée Ehresmann · French digital mathematics library (Numdam) · 1997
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.