error: invalid initialization of reference of type 'int&' from expression of type 'const int'

obj is a const reference. object is a non-const reference.

You can't initialize a non-const reference from a const reference, because doing so would defeat the purpose of having a const reference in the first place.

If you want your instance of Object to be able to modify the int that's passed to its constructor, then the constructor should take a non-const reference. If you don't, then the data member should be a const reference.

In any case, you are storing up trouble for yourself if you use new to allocate objects that have references as data members. It's your problem to ensure that you delete the Object before i goes out of scope (or anyway, ensure that the Object doesn't use its member object after i goes out of scope.

You are trying to assign a const reference to a non const reference. This means that your Object class can modify the content of object.

const int myConstNumber = 4;
Object<int> intObj(myConstNumber);

intObj.object = 3; // you have indirectly modified the value of myConstNumber

C++ doesn't let you do that. You can make a copy of the object or add the const to your attribute.

template <class T>
class Object : public Container {
public:
    T object; // valid

or

template <class T>
class Object : public Container {
public:
    const T& object; // valid

in this case you won't be able to modify object