The paper proposes a number of models to examine through what mech-anisms a population of autonomous agents could arrive at a repertoire of perceptually grounded categories that is sufficiently shared to allow successful communication. The models are inspired by the main approaches to human categorisation being discussed in the literature: nativism, empiricism, and culturalism. Colour is taken as a case study. Although the paper takes no stance on which position is to be accepted as final truth with respect to hu-man categorisation and naming, it points to theoretical constraints that make each position more or less likely and contains clear suggestions on what the best engineering solution would be. Specifically, it argues that the collective choice of a shared repertoire must integrate multiple constraints, including constraints coming from communication.