ScalingStacks

Remark 4.3. The globular sets considered here are sometimes called reflexive globular sets, in order to emphasize the fact that our globular category $\mathbb{G}_{n}$ includes degeneracies $C_{k}\to C_{k-1}$. The non-reflexive globular category $\mathbb{G}_{n}^{\textrm{nr}}$ consists of the subcategory of $\mathbb{G}_{n}$ with the same objects but only with the morphisms which are injective on $n$-morphisms. As a category it is generated by object $C_{k}$ $0\leq k\leq n$ with morphisms

$$s_{k},t_{k}:C_{k-1}\to C_{k}$$

satisfying $s_{k}t_{k-1}=t_{k}t_{k-1}$ and $s_{k}s_{k-1}=t_{k}s_{k-1}$. We will have only cursory use for non-reflexive globular sets in this paper.