  In this article, we construct a cofibrantly generated model structure on the
category of spaces stratified over a fixed poset, and show that it is
Quillen-equivalent to a category of diagrams of simplicial sets. Then,
considering all those model structures together, we construct a cofibrantly
generated model structure on the category of all stratified spaces. In both
model categories, weak-equivalences are characterized by stratified homotopy
groups.
