# The Word Problem for Double Categories

*Antonin Delpeuch*

### Abstract

We solve the word problem for double categories by translating it to the word problem for 2-categories. This yields a quadratic algorithm deciding the equality of diagrams in a free double category. The translation is of interest in its own right since and can for instance be used to reason about double categories with the language of 2-categories, sidestepping the pinwheel problem.

Annote

Comment: Feedback welcome!

Journal

arXiv:1907.09927 [cs‚ math]

Keywords

18D05‚Computer Science − Logic in Computer Science‚Mathematics − Category Theory

Month

jul

Year

2019