Higher Categories and Slices of Globular Operads

Abstract

In an unpublished preprint \cite{batanin}, Batanin conjectures that it is possible to take `slices' of a globular operad, thereby isolating the algebraic structure in each dimension. It was further hypothesised that the slices of a globular operad for some theory of higher category contain essential information about those higher categories, namely whether or not they are equivalent to the fully weak variety. In this paper, we use the theory of presentations for globular operads developed in \cite{Me} to provide a concrete definition of slices, and calculate the slices for several key theories of $n$-category.

arXiv admin note: text overlap with arXiv:2101.00077