Polycategories via pseudo-distributive laws

In this paper, we give a novel abstract description of Szabo's polycategories. We use the theory of double clubs – a generalisation of Kelly's theory of clubs to ‘pseudo’ (or ‘weak’) double categories – to construct a pseudo-distributive law of the free symmetric strict monoidal category pseudocomonad on Mod over itself qua pseudomonad, and show that monads in the ‘two-sided Kleisli bicategory’ of this pseudo-distributive law are precisely symmetric polycategories.