string diagrams are two

Last updated Jul 23, 2024

There are two different adjunctions below the category of monoidal categories that make string diagrams a universal language.

We can consider the forgetful functor to polygraphs, or monoidal signatures. The left adjoint builds classical string diagrams where we must only use wires and generators. This is a strict 1-adjunction.
We can consider the forgetful functor to monoidal graphs, which are polygraphs where objects form themselves a monoid. This constructs This is a 2-adjunction.