String diagram

Summary

A string diagram is a picture of a morphism in a monoidal category: wires stand for objects and boxes stand for morphisms. Composition is drawn by stacking boxes and the monoidal product by placing them side by side. A theorem of Joyal and Street says that diagrams that deform into each other in the plane, with wires kept upward, denote the same morphism. So many computations with coherence isomorphisms become moves of pictures.