The company owned all of the industries needed to create steel.
Vertical integration is an economic method of buying or creating companies that are needed to create another product. A vertical monopoly would suggest the company has bought all of the supply companies and control all of the production of the product in question.
Carnegie used vertical integration to create steel at a lower price than other companies. He owned iron mines and railroad companies so he was able to access the iron used to make the steel and then use his own railroad companies to transport his company's steel. With this process, no other company could produce steel as cheaply as Carnegie could and that allowed Carnegie to buyout other steel companies as well.
