Biprops are bicategories with free-monoid objects and symmetric tensor-like structure; symmetric weak multicategories and their multifunctors map functorially to biprops and their morphisms.
Bartlett, Quasistrict symmetric monoidal 2-categories via wire diagrams , 2014
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Biprops
Biprops are bicategories with free-monoid objects and symmetric tensor-like structure; symmetric weak multicategories and their multifunctors map functorially to biprops and their morphisms.