There are many different approaches to weak higher-dimensional categories. One proposed by Leinster, based on an idea of Batanin's, defines weak ω-categories as the algebras for a particular monad on the category of globular sets. Intuitively, this monad encodes only the existence part of the pasting theorem for globular pasting diagrams. In this talk, I will make precise (and sketch a proof of) the uniqueness part, and discuss some of its applications. This talk is based on joint work with Soichiro Fujii (Macquarie University) and Keisuke Hoshino (Kyoto University), and it's a longer version of the talk I will be giving at the AustMS.