Geodesic
The word problem for double categories
Theory and applications of categories, Tome 35 (2020), pp. 1-18

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a0/}
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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/