A Category of Surface-Embedded Graphs
Logic in Computer Science
2023-08-01 v2
Abstract
We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in a non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is a new formulation of double pushout rewriting on graphs which explicitly records the boundary of the rewrite. Using this boundary structure we can augment these graphs with a rotation system, allowing the surface topology to be incorporated.
Cite
@article{arxiv.2210.08914,
title = {A Category of Surface-Embedded Graphs},
author = {Malin Altenmüller and Ross Duncan},
journal= {arXiv preprint arXiv:2210.08914},
year = {2023}
}
Comments
In Proceedings ACT 2022, arXiv:2307.15519