A (multicolored) PROP can also be described as a polycategory; what distinguishes a polycategory from a PROP is that in a polycategory, we can only compose along one object at once. That is, we have a composition operation
Some categorical structures that are normally defined in a monoidal category can instead be defined in a polycategory, including Frobenius algebras and dual objects. Dual objects, in particular, are a form of “negation” that make a linearly distributive category into a star-autonomous category.
M.E. Szabo, Polycategories, Comm. Algebra 3 (1975) 663-689. DOI