ScalingStacks

A closed model category is said to be proper if

1. (1)

   the pushout of a weak equivalence along a cofibration is a weak equivalence, and

2. (2)

   the pullback of a weak equivalence along a fibration is a weak equivalence.

The Reedy model category structure is proper, because cofibrations and fibrations are in particular cofibrations and fibrations in each degree, and ${\operatorname{\mathcal{S}}}$ is proper.