Consider the following snippet:

public static void main(String[] args) {
        Function<String, String> function = String::toUpperCase;        //OK
//        Comparator<String> comparator = String::toUpperCase;          //Compilation error(makes sense, as String.toUpperCase(Locale locale) & String.toUpperCase() are not compatible)
        fun(String::toUpperCase);                                       // java: reference to fun is ambiguous
    }

    public static void fun(Function<String, String> function) { // String apply(String obj)
        System.out.println("Function");
    }

    public static void fun(Comparator<String> comparator) {     // int compare(String s1, String s2)
        System.out.println("Comparator");
    }

I’m failing to understand the reason behing ambiguity error for method invocation fun(String::toUpperCase).

As, both of the overloaded versions of String::toUpperCase themselves are not compatible with int compare(String s1, String s2) from the Comparator class, then how come the compiler complains about ambiguity in the first place?

Am I missing something here?