Simple string diagrams and n-sesquicategories

Manuel Araújo

We define a monad T_n^D^* whose operations are encoded by simple string diagrams and we define n-sesquicategories as algebras over this monad. This monad encodes the compositional structure of n-dimensional string diagrams. We give a generators and relations description of T_n^D^*, which allows us to describe n-sesquicategories as globular sets equipped with associative and unital composition and whiskering operations. One can also see them as strict n-categories without interchange laws. Finally we give an inductive characterization of n-sesquicategories.

Keywords: string diagrams, higher categories

2020 MSC: 18N20, 18N30

Theory and Applications of Categories, Vol. 38, 2022, No. 34, pp 1284-1325.

Published 2022-11-15.

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