Class template with template class friend, what’s really going on here?

by 
template<class T> class BE{
  template<class T> friend class BT;
};

Is not allowed because template parameters cannot shadow each other. Nested templates must have different template parameter names.

template<typename T>
struct foo {
  template<typename U>
  friend class bar;
};

This means that bar is a friend of foo regardless of bar‘s template arguments. bar<char>, bar<int>, bar<float>, and any other bar would be friends of foo<char>.

template<typename T>
struct foo {
  friend class bar<T>;
};

This means that bar is a friend of foo when bar‘s template argument matches foo‘s. Only bar<char> would be a friend of foo<char>.

In your case, friend class bar<T>; should be sufficient.

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