Biprops

TL;DR

The paper introduces biprops, a new mathematical structure generalizing coloured props and symmetric weak multicategories, and establishes a functorial relationship between symmetric weak multicategories and biprops.

Contribution

It defines biprops as a novel bicategory framework and proves a functorial correspondence with symmetric weak multicategories.

Findings

Biprops generalize coloured props and symmetric weak multicategories.

A symmetric weak multicategory induces a biprop.

A symmetric weak multifunctor induces a morphism of biprops.

Abstract

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.