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 (2010)
Benjamin Hummon. Surface diagrams for gray-categories, Phd Thesis, UC San Diego (2012) [escholar:5b24s9cc, pdf]
John Barrett, Catherine Meusburger, Gregor Schaumann: Gray categories with duals and their diagrams, Advances in Mathematics 450 (2024) 109740 [arXiv:1211.0529, doi:10.1016/j.aim.2024.109740]
Christoph Dorn, Christopher Douglas: Manifold diagrams and tame tangles (2022) [arXiv:2208.13758]
(via manifold diagrams)
Last revised on September 1, 2024 at 14:17:13. See the history of this page for a list of all contributions to it.