In order to be able to use a class as the key in a map, all that is required of the key is that it be copiable and assignable. The ordering within the map is defined by the third argument to the template (and the argument to the constructor, if used). This defaults to std::less<KeyType>, which defaults to the \< operator, but there’s no requirement to use the defaults. Just write a comparison operator (preferably as a functional object):

struct CmpMyType
{
    bool operator()( MyType const& lhs, MyType const& rhs ) const
    {
        //  ...
    }
};

In C++, the “compare” predicate must be a strict weak ordering. In particular, compare(X,X) must return false for any X. i.e. if CmpMyType()(a, b) returns true, then CmpMyType()(b, a) must return false, and if both return false, the elements are considered equal (members of the same equivalence class).

Strict Weak Ordering

This is a mathematical term to define a relationship between two objects.

Its definition is:

Two objects x and y are equivalent if both f(x, y) and f(y, x) are false. Note that an object is always (by the irreflexivity invariant) equivalent to itself.

In terms of C++ this means if you have two objects of a given type, you should return the following values when compared with the operator <.

X    a;
X    b;

Condition:                  Test:     Result
a is equivalent to b:       a < b     false
a is equivalent to b        b < a     false

a is less than b            a < b     true
a is less than b            b < a     false

b is less than a            a < b     false
b is less than a            b < a     true

How you define equivalent/less is totally dependent on the type of your object.