Computads and string diagrams for n-sesquicategories
Published in cahiers de topologie et géométrie différentielle catégoriques, 2024
An $n$-sesquicategory is an $n$-globular set with strictly associative and unital composition and whiskering operations, which are however not required to satisfy the Godement interchange laws which hold in $n$-categories. In a previous paper we showed how these can be defined as algebras over a monad whose operations are simple string diagrams. In this paper, we give an explicit description of computads for this monad and we prove that the associated category of computads is a presheaf category. We use this to describe a string diagram notation for representing arbitrary composites in $n$-sesquicategories. This is a step towards a theory of string diagrams for semistrict $n$-categories.