String Diagrams For Double Categories and Equipments
Abstract
A popular graphical calculus for monoidal categories makes computations tactile and intuitive. Complicated diagram chases can be expressed in a few pictures and discovered by playing with a shoelace. Joyal and Street's proof of the soundness of this calculus says that any deformation of a diagram, any bending of the strings, describes the same morphism. In this paper, we extend the graphical calculus to double categories and proarrow equipments in order to bring the string diagrammatic method to formal category theory. Our main theorem proves this calculus sound with the help of Dawson and Pare's results on composition in double categories.
Cite
@article{arxiv.1612.02762,
title = {String Diagrams For Double Categories and Equipments},
author = {David Jaz Myers},
journal= {arXiv preprint arXiv:1612.02762},
year = {2018}
}
Comments
33 pages. Regarding previous versions: the sections on virtual equipments and the embedding theorem will appear as a separate paper