Global function definition in header file - how to avoid duplicated symbol linkage error

Use the inline keyword.

inline std::ostream& operator<< (std::ostream& o, const error_code& e) {
    return o << "[" << e.hi << "," << e.lo << "]";
}

Either make the function inline:

inline std::ostream& operator<< (std::ostream& o, const error_code& e) {
    return o << "[" << e.hi << "," << e.lo << "]";
}

or make it a template function:

template<class Ch, class Tr>
std::basic_ostream<Ch,Tr>& operator<< (std::basic_ostream<Ch,Tr>& o,
                                       const error_code& e) {
    return o << "[" << e.hi << "," << e.lo << "]";
}

You can make the function static. It specifies internal linkage, so the linker won't care if the function is already defined in other translation units.

Or, as already mentioned, you can make it inline. It still has external linkage, but the standard allows external inline functions to have a definition in multiple translation units.