Geodesic
The word problem for double categories
Theory and applications of categories, Tome 35 (2020), pp. 1-18
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We solve the word problem for free double categories without equations between generators 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. It also shows that although double categories are formally more general than 2-categories, they are not actually more expressive, explaining the rarity of applications of this notion.

Publié le :
Classification : 18D05
Keywords: double categories, word problem, string diagrams 
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     author = {Antonin Delpeuch},
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Antonin Delpeuch. The word problem for double categories. Theory and applications of categories, Tome 35 (2020), pp. 1-18. http://geodesic.mathdoc.fr/item/TAC_2020_35_a0/