Biprops

We define biprops as a generalization of coloured props and of symmetric weak multicategories. These are bicategories whose objects form a free monoid. They are equipped with some structure resembling a symmetric strict tensor product. We prove that a symmetric weak multicategory gives rise to a biprop and a symmetric weak multifunctor gives rise to a morphism of biprops. This is a functor from the category of symmetric weak multicategories to the category of biprops.