  Bayesian networks are widely utilised in various fields, offering elegant
representations of factorisations and causal relationships. We use surjective
functions to reduce the dimensionality of the Bayesian networks by combining
states and study the preservation of their factorisation structure. We
introduce and define corresponding notions, analyse their properties, and
provide examples of highly symmetric special cases, enhancing the understanding
of the fundamental properties of such reductions for Bayesian networks. We also
discuss the connection between this and reductions of homogeneous and
non-homogeneous Markov chains.
