c++ will `map::key_comp` hamper performance if called as a way to compare a number with existing key?

i have a type defined as below,

using BookMapT = std::map<long long int, long long int, std::function<bool(long long int,long long int)>>;
BookMapT greater_map(greater<long long int>{});
BookMapT less_map(less<long long int>{});

So if have a number and I want to compare with the beginning of a BookMapT

int compare(BookMapT& book, long long int number_to_compare){
    return book.key_comp()(number_to_compare, book.begin()->first);
}

From http://www.cplusplus.com/reference/map/map/key_comp/ I can see key_comp return a copy of the comparison object, will this copy action somehow hamper performance? What confuse me most is how much cost is this copying of std::function ?

Thanks.