string diagrams are the internal language of monoidal categories
There exists an adjunction between
polygraphs A polygraph signature, $𝓖$, is given by a set of objects, $𝓖{\mathrm{obj}}$, and a set of polyedges $𝓖(X₁,...,Xₙ; Y₁,...,Yₘ)$ for...
and
strict monoidal categories whose left adjoint is given by
string diagrams.Polygraph