Why comparator of std::map must be const?

Question

I've wrote comparator functional object for std::map for comparing string without case sensitivity.

class CaseInsensitiveCmp
{
public:
    bool operator() (const std::string& op1, const std::string& op2) const
    {
        std::string op1low(op1.size(),'c'), op2low(op2.size(),'c');
        std::transform(op1.begin(), op1.end(),op1low.begin(),::tolower);
        std::transform(op2.begin(), op2.end(),op2low.begin(),::tolower);
        return op1low<op2low;
    }
};

The problem is, that if the member function (operator() ) is not const function i.e.

 bool operator() (const std::string& op1, const std::string& op2);

The compiler XLC compiler generates en error

CaseInsensitiveCmp::operator()(const std::string &, const std::string &)" is not a viable candidate.

Can anyone refer to any point in c++ standard that says that comparison functional object member function must be const?