Sending a session cookie in the response

In page 231 of HFSJ you can read:
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Sending a session cookie in the response
HttpSession session = request.getSession();

... everything else happens automatically.
...
You don't set the Cookie into the response (under the Set-Cookie header).
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Since the getSession() method doesn't have any reference to the response, I don't understand how this method can set a cookie into the response.

Anybody has an explanation?

I will try to attempt this question.

The container is the one who provides the servlet with reference to request and response objects it creates. so, obviously the container will have a reference to the response object, until the response is completely written to the client. Then both request and response may be GC-ed.

I think this is done by the container by "adding a header containing cookie object" in response object.

The container might do it this way:

Of course, the container has references to request / response and other objects.

Thanks