To have complete control over something, so others can't have any.
Monopolize can make people think of unfairness or being greedy.
Examples:
The big company tries to monopolize the market.
She doesn't want to share, so she tries to monopolize the game.
He monopolizes the conversation, so no one else can talk.
The cat monopolizes the sunny spot on the floor.
The evil king tries to monopolize all the gold in the kingdom.
She always monopolizes the swing at the park.