String diagrams

Intuition

String diagrams are made of boxes${\displaystyle f:x\to y}$, which represent processes, with a list of wires${\displaystyle x}$ coming in at the top and ${\displaystyle y}$ at the bottom, which represent the input and output systems being processed by the box ${\displaystyle f}$. Starting from a collection of wires and boxes, called a signature, one may generate the set of all string diagrams by induction: