We give a homotopy theoretic characterization of sheaves on a stack and, more generally, a presheaf of groupoids on an arbitary small site . We use this to prove homotopy invariance and generalized descent statements for categories of sheaves and quasi-coherent sheaves. As a corollary we obtain an alternate proof of a generalized change of rings theorem of Hovey.
"Descent for quasi-coherent sheaves on stacks." Algebr. Geom. Topol. 7 (1) 411 - 437, 2007. https://doi.org/10.2140/agt.2007.7.411