Homomorphisms of separoids

The notion of separoid homomorphisms was introduced in [Nešetřil, J., and R. Strausz, Universality of separoids, Arch. Math. (Brno) 42 (2006), 85–101], by Jarik Nešetřil and the author, where it was proved that separoids endowed with such maps constitute a dense and universal category. Using results developed there, it will be showed here that, when restricted to point separoids, there is no finite duality. Some open problems are proposed.