# Do mixed Hodge modules form a stack?

The question should be reasonably self-contained: do MHM's form a stack? This is well-known for perverse sheaves, proved already in [BBD(G)]; does it hold for mixed Hodge modules? In other words, if I have a variety $X$ over the complex numbers, an open cover $(U_i)$ and mixed Hodge modules on all the $U_i$ with gluing isomorphisms on overlaps with the obvious cocycle condition, then do I get a unique MHM on $X$? I would like this in the analytic category but a reference for algebraic varities over the complex numbers is likely to satisfy me.

-