We exhibit a 5-uniform hypergraph that has no polychromatic 3-coloring, but
all its restricted subhypergraphs with edges of size at least 3 are
2-colorable. This disproves a bold conjecture of Keszegh and the author, and
can be considered as the first step to understand polychromatic colorings of
hereditary hypergraph families better since the seminal work of Berge. We also
show that our method cannot give hypergraphs of arbitrary high uniformity, and
mention some connections to panchromatic colorings