Simple string diagrams and n-sesquicategories
Published in Theory and Applications of Categories, 2022
We define a monad on $n$-globular sets 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 this monad, 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.