bpo-32362: Fix references to non-existent multiprocessing.Connection() (GH-6223)

(cherry picked from commit 9f3535c9cd)

Co-authored-by: Bo Bayles <bbayles@gmail.com>

Doc/library/multiprocessing.rst

@@ -735,8 +735,9 @@ For an example of the usage of queues for interprocess communication see
 
 .. function:: Pipe([duplex])
 
-   Returns a pair ``(conn1, conn2)`` of :class:`Connection` objects representing
-   the ends of a pipe.
+   Returns a pair ``(conn1, conn2)`` of
+   :class:`~multiprocessing.connection.Connection` objects representing the
+   ends of a pipe.
 
    If *duplex* is ``True`` (the default) then the pipe is bidirectional.  If
    *duplex* is ``False`` then the pipe is unidirectional: ``conn1`` can only be
@@ -1021,10 +1022,13 @@ Miscellaneous
 Connection Objects
 ~~~~~~~~~~~~~~~~~~
 
+.. currentmodule:: multiprocessing.connection
+
 Connection objects allow the sending and receiving of picklable objects or
 strings.  They can be thought of as message oriented connected sockets.
 
-Connection objects are usually created using :func:`Pipe` -- see also
+Connection objects are usually created using
+:func:`Pipe <multiprocessing.Pipe>` -- see also
 :ref:`multiprocessing-listeners-clients`.
 
 .. class:: Connection
@@ -1159,6 +1163,8 @@ For example:
 Synchronization primitives
 ~~~~~~~~~~~~~~~~~~~~~~~~~~
 
+.. currentmodule:: multiprocessing
+
 Generally synchronization primitives are not as necessary in a multiprocess
 program as they are in a multithreaded program.  See the documentation for
 :mod:`threading` module.
@@ -2269,7 +2275,7 @@ Listeners and Clients
    :synopsis: API for dealing with sockets.
 
 Usually message passing between processes is done using queues or by using
-:class:`~multiprocessing.Connection` objects returned by
+:class:`~Connection` objects returned by
 :func:`~multiprocessing.Pipe`.
 
 However, the :mod:`multiprocessing.connection` module allows some extra
@@ -2299,7 +2305,7 @@ multiple connections at the same time.
 .. function:: Client(address[, family[, authkey]])
 
    Attempt to set up a connection to the listener which is using address
-   *address*, returning a :class:`~multiprocessing.Connection`.
+   *address*, returning a :class:`~Connection`.
 
    The type of the connection is determined by *family* argument, but this can
    generally be omitted since it can usually be inferred from the format of
@@ -2349,8 +2355,8 @@ multiple connections at the same time.
    .. method:: accept()
 
       Accept a connection on the bound socket or named pipe of the listener
-      object and return a :class:`~multiprocessing.Connection` object.  If
-      authentication is attempted and fails, then
+      object and return a :class:`~Connection` object.
+      If authentication is attempted and fails, then
       :exc:`~multiprocessing.AuthenticationError` is raised.
 
    .. method:: close()
@@ -2386,7 +2392,7 @@ multiple connections at the same time.
    For both Unix and Windows, an object can appear in *object_list* if
    it is
 
-   * a readable :class:`~multiprocessing.Connection` object;
+   * a readable :class:`~multiprocessing.connection.Connection` object;
    * a connected and readable :class:`socket.socket` object; or
    * the :attr:`~multiprocessing.Process.sentinel` attribute of a
      :class:`~multiprocessing.Process` object.
@@ -2509,10 +2515,10 @@ an ``'AF_PIPE'`` address rather than an ``'AF_UNIX'`` address.
 Authentication keys
 ~~~~~~~~~~~~~~~~~~~
 
-When one uses :meth:`Connection.recv <multiprocessing.Connection.recv>`, the
+When one uses :meth:`Connection.recv <Connection.recv>`, the
 data received is automatically
-unpickled.  Unfortunately unpickling data from an untrusted source is a security
-risk.  Therefore :class:`Listener` and :func:`Client` use the :mod:`hmac` module
+unpickled. Unfortunately unpickling data from an untrusted source is a security
+risk. Therefore :class:`Listener` and :func:`Client` use the :mod:`hmac` module
 to provide digest authentication.
 
 An authentication key is a byte string which can be thought of as a