nLab surface diagram




Surface diagrams categorify string diagrams: while string diagram calculus describes the composition of morphisms in 2-categories, surface diagram calculus describes composition of morphisms in (non-strict) 3-categories.


There are several discussions and variation of surface diagrams available.

While all of the above notions are “in essence” equivalent, they differ in some of their technical details.


  • Todd Trimble, Surface diagrams

  • John Barrett, Catherine Meusburger, Gregor Schaumann. Gray categories with duals and their diagrams. arXiv

  • Benjamin Hummon. Surface diagrams for gray-categories. Phd Thesis, UC San Diego. pdf

  • Christoph Dorn and Christopher Douglas, Manifold diagrams and tame tangles, 2022 (arXiv)

Last revised on March 9, 2023 at 12:02:34. See the history of this page for a list of all contributions to it.