Then you do not understand monopolies. They reduce innovation, they do not increase innovation, because competition is reduced. As such, patents and copyrights reduce innovation and so inventions are delayed or we do not get them at all.
Of course I understand monopolies. I understand that there's a huge incentive to get a monopoly, because then you don't have to compete on things like price and efficiency of production and distribution. In fact, the incentive is so great that people will invest a lot of research money to come up with new inventions that they can patent and get monopolies on. Compare that to the situation where someone invests a lot of money in an invention, starts selling it, and then has a bunch of competitors come along and spend far less money reverse-engineering it than he spent inventing it... That is why patents encourage innovation.
Now once someone has a patent, there aren't the same kind of competitive pressures as there usually are when it comes to manufacturing, distributing, advertising, etc. Of course, most patents don't really lead to market domination, for the simple reason that there are few things that can only be done one way. If I have a patent on a new thing called a paper clip, I still have to worry about competing with that guy who came up with the banker's clip. In fact, there's a hint about another way patents encourage innovation: they force people to come up with different ways of doing the same thing, instead of just competing for more market share with the same product.