An example of a Fraïssé class without a Katětov functor

We disprove a conjecture from [W. Kubiś, D. Mašulović, Katětov functors, preprint, http://arxiv.org/abs/1412.1850] by showing the existence of a Fraïssé class $\mathcal{C}$ which does not admit a Katětov functor. On the other hand, we show that the automorphism group of the Fraïssé limit of $\mathcal{C}$ is universal, as it happens in the presence of a Katětov functor.

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