precipitation reaction - cellulose in schweizer reagent reacts with acid
It's possible to regenerate cellulose from Schweizer's reagent by dilution in plain water, though neutralization of the high pH+ cuprammonium solution with an acid is more efficient. $\ce{HCl}$ works as well as $\ce{H2SO4}$. Economics probably drives the choice.

The chemistry is based on breaking cellulose, a polysaccharide (polymer)  β(1→4) linked D-glucose, into smaller, soluble, segments, and reconstituting the longer polysaccharide through neutralization.