> Monopolists, however, ignore the demand curve.

That doesn't make sense, to obtain the MIR monopolists have to have an implicit consideration of the demand curve. Monopolists can't push the price off the demand curve without pointlessly leaving arbitrage opportunities (or burning money, I suppose) and their revenue depends on price and quantity.

There is a fun thought experiment too if we consider a silly degenerate case, imagine the demand curve has a practically impossible shape and spikes to infinite price at 10 widgets. Any logically sound strategy will tell the monopolist to produce 10 widgets because profit would be infinite. So they can't ignore a demand curve in theory because at a minimum they have to care that it is not a degenerate case.

Monopolists base production on their costs and revenue, not supply and demand. Both "supply" and "demand" are real things—that monopolists ignore if it profits them.