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).

References

• Edwards, David A.; Hastings, Harold M. (1980), "Čech theory: its past, present, and future", The Rocky Mountain Journal of Mathematics, 10 (3): 429–468, doi:10.1216/RMJ-1980-10-3-429, MR 0590209.
• Edwards, David A.; Hastings, Harold M. (1976), Čech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Mathematics, Vol. 542, Springer-Verlag, Berlin-New York, MR 0428322.