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The word problem for double categories

##
Antonin Delpeuch

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.

Keywords:
double categories, word problem, string diagrams

2010 MSC:
18D05

*Theory and Applications of Categories,*
Vol. 35, 2020,
No. 1, pp 1-18.

Published 2020-01-02.

http://www.tac.mta.ca/tac/volumes/35/1/35-01.pdf

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