The petit topos of globular sets

There are now several definitions of weak ω-category [1,2,5,19]. What is pleasing is that they are not achieved by ad hoc combinatorics. In particular, the theory of higher operads which underlies Michael Batanin's definition is based on globular sets. The purpose of this paper is to show that many of the concepts of [2] (also see [17]) arise in the natural development of category theory internal to the petit¹ topos Glob of globular sets. For example, higher spans turn out to be internal sets, and, in a sense, trees turn out to be internal natural numbers.