Categorifying the ZX-calculus

Understand

We build a symmetric monoidal and compact closed bicategory by combining spans and cospans inside a topos.

• This can be used as a framework in which to study open networks and diagrammatic languages.
• We illustrate this framework with Coecke and Duncan's zx-calculus by constructing a bicategory with the natural numbers for 0-cells, the zx-calculus diagrams for 1-cells, and rewrite rules for 2-cells.