forward declaration of std::ostream

The files are organized as following:

//MyClass.h
#pragma once
namespace std {
    class ostream;
};
class MyClass
{
private:
    int a;
public:
    friend std::ostream& operator<<(std::ostream& o, const MyClass& obj);
};

//MyClass.cpp
#include<iostream>
std::ostream& operator<<(std::ostream& o, const MyClass& obj)
{
    o << obj.a << std::endl;
    return o;
}

//main.cpp
#include"MyClass.h"
#include<iostream>

int main()
{
    MyClass obj;
    std::cout << obj;
}

It failed compiling with errors on overloading operator<<:

Error C2371 'std::ostream': redefinition; different basic types

What's the issue here and how to correct it?

As other people noted, ostream is not a class but an alias to a template instantiation, basically ostream = basic_ostream<char>. This is an implementation detail of the standard library; it's there because it needs to support also wostream (which is basic_ostream<wchar_t>) and possibly other stream types. But other implementations may do it differently (using e.g. source code generation) or very differently (distributing pre-compiled modules). You should not depend on any particular implementation.

You should not declare anything inside the std namespace (except stuff which the C++ Standard explicitly permits). To forward-declare ostream and such, use #include <iosfwd> in your header file.

Alternatively, just do #include <iostream> instead of forward declaration — less technical details to remember vs slightly slower compilation — do your own judgment on what is better.