The keys in the Map are internally Set and can be retrieved in a Set. Since Set doesn't allow duplicates the key values in Map are also not allowed to contain the duplicates. But the values in Map can be duplicate.
Yes Maps also fall under the collection category although they dont explicitly implement the Collection interface. So the right answer would be List. By the way Maps do not reject the new duplicate value. The new value will replace the previous one. In Sets the add method will return false when you try to add a new value.