A fast-curing mineral binder mixture includes a titanium(IV)-based accelerator, a cement which includes at least one component which is selected from the compounds 3CaO*Al2O3, 12CaO*7Al2O3, CaO*Al2O3, CaO*2Al2O3, CaO*6Al2O3 and 4CaO*3Al2O3*SO3, and 15 to 80 wt % of a sulfate carrier, wherein the wt % is based on a weight of the fast-curing mineral binder mixture. The fast-curing mineral binder mixture can optionally include at least one alkaline component and/or at least one additive.