Wealth is definitely a big part of what a monopoly is. It has to do with the means of production too.
Example: The Most Serene Republic of Venice has a monopoly on trade between the Trebizond (end point of the Silk Road) and Italy. They carry out this trade with an extensive fleet of hundreds of ships. The Bishop of Rome would like to join in on this lucrative trade, but lacks ships, because his predecessors have placed their focus on building large cathedrals, promoting great artists, and launching inquisitions.
Now, the Pope can spend a fortune building up the necessary navy and merchant marine to conduct Eastern trade. Through the sale of indulgences across Europe, he does have a massive fortune, perhaps more than the Venetians.' But it is nonetheless much more expensive for him to enter this trade than for the Venetians to continue doing it, so he probably won't.
If the Pope is vastly more rich than the Venetians, he might try it anyway and dare Venice to try to cut prices. But that's not surprising, because concentration of wealth in the hands of one person is closely related to that person having a monopoly. A monopoly is power. Wealth can give you power. So it's not strange that all that wealth can buy you a monopoly.
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