on the inhomogeneous Markov chain structure of the model. LM would like to thanks Dorian Ni for his feedback on the model.

Presentation of the mathematical model {#sec:modelPres}
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In this section, we shall present the model describing the evolution of knowledge within a finite population. Many different definitions of knowledge have been proposed. Here, we consider that knowledge results from conceptualizations that appropriately reflect the structure of the world and model *conceptualization* as functions linking a set of possible experiences to a set of possible concepts. We call these functions *knowledge-like functions*.

Time is supposed discrete. At each time step the knowledge-like function of individuals changes according to a learning dynamic that depends on both social and individual learning. Our model is an extension of the model of Cucker, Smale and Zhou describing the evolution of language [@CuckerSmale2004], and can be seen as an hybrid between a learning algorithm [@CuckerSmale2001] and an individual based model [@AmbrosioFornasierMorandottiSavare2018; @Albi2019vehicular]. We suppose that each individual influences each other through a social learning matrix $\Lambda \in \mathcal{M}_N({\mathbb{R}})$. This matrix depends on both the structure of the population (*e.g.* a professor has a strong impact on its students, while students have less impact on 