Pro-simplicial set

In mathematics, a pro-simplicial set is an inverse system of simplicial sets.
A pro-simplicial set is called "pro-finite" if each term of the inverse system of simplicial sets has finite homotopy groups.
Pro-simplicial sets show up in shape theory, in the study of localization and completion in homotopy theory, and in the study of homotopy properties of schemes (e.g. étale homotopy theory).