Abstract :
There are now several definitions of weak ω-category [1, 2, 5 and 19]. What is pleasing is that they are not achieved by ad hoc combinatorics. In particular, the theory of higher operads which underlies Michael Bataninʹs 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 petit 1 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.
