In the usual sense a globular set consists of objects, arrows between objects, 2-arrows between arrows, etc. having $n$-arrows for every $n \in \mathbb N$ (although some may be empty). A category (or an $(\infty,1)$-category for that matter) is a globular set with some additional structure.
Does anyone ever consider "infinitely deep" globular sets? In the sense that there are no objects, just an infinite chain of $n$-arrows for $n \in \mathbb Z$ which point between $(n-1)$-arrows? And if one were to form an "infinitely deep" category like this (yes the associativity isomorphism constraints are horrendously complicated), do the results of usual category theory even hold?