String Diagrams For Double Categories and Equipments

Publication date: 8 December 2016

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.

Has companion code repository: https://github.com/varkor/tangle

Mathematics Subject Classification ID

General theory of categories and functors (18A99)

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