David Kern: ω-categories are algebras in infinitely iterated spans

Abstract:

In 1998, Batanin used complex constructions to produce his algebraic definition of weak ω-categories as algebras in iterated spans over a sufficiently contractible operad. Through the following decades, the advent of homotopy-coherent algebra has made the theory of ω-categories much more approachable. I will explain how, thanks to the homotopical language, we can understand ω-categories as associative algebras in iterated spans using only simple constructions.