This article proposes a number of models to examine through which mechanisms 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 we take no stance on which position is to be accepted as final truth with respect to human categorisation (...) and naming, we do point to theoretical constraints that make each position more or less likely and we make clear suggestions on what the best engineering solution would be. Specifically, we argue that the collective choice of a shared repertoire must integrate multiple constraints, including constraints coming from communication. Key Words: autonomous agents; colour categorisation; colour naming; connectionism; cultural evolution; genetic evolution; memes; origins of language; self-organisation; semiotic dynamics; symbol grounding. (shrink)