Put simply, competition destroys a monopoly.
Monopoly is a market structure in which there is only one seller with access to a given market. This seller may have the monopoly because the market is naturally a monopoly or the seller may have it because there are rules that bar competition. Either way, there is no competition in a monopoly.
If competition is introduced, the monopoly is, by definition, destroyed. The market moves from being a monopoly to being something else, most likely a market in which there is monopolistic competition. So, competition affects a monopoly by destroying it.