A duopoly is superficially similar to a monopoly. A duopoly is a market that has only two suppliers, or a market that is dominated by two suppliers to the extent that they jointly control prices.
Unless the two suppliers act in concert (which would be illegal in most countries) there is likely to be competition in a duopolistic market. Rather than being similar to a monopoly, it is the simplest case of an oligopoly.
However, this competition is likely to be limited, leading to higher prices, and a worse deal for consumers in other ways, than in a truly competitive market.