Min and Max of a list of Associations

How about

a = {
    <|"a" -> 4, "b" -> 9, "c" -> 15|>,
    <|"a" -> 21, "b" -> 11, "c" -> 1|>,
    <|"a" -> 12, "b" -> 3, "c" -> 21|>
};

Merge[a, Min]

(*<|"a" -> 4, "b" -> 3, "c" -> 1|>*)

Merge[a, Max]

(*<|"a" -> 21, "b" -> 11, "c" -> 21|>*)

EDIT

Improved, as per Kuba's suggestion.

Random`Private`MapThreadMin[x]
Random`Private`MapThreadMax[x]

<|"a" -> 4, "b" -> 3, "c" -> 1|>

<|"a" -> 21, "b" -> 11, "c" -> 21|>