David Roberts
Delta-space

The simplex category $\Delta$ has a subcategory ${\Delta }_i$ consisting of the same objects and only the injective maps

$$n\to n\prime$$n \to n'

where $n\prime >n$. A $\Delta$-space is a functor

$${\Delta }_i^{\mathrm{op}}\to \mathrm{Top}.$$\Delta_i^{op} \to Top.