If pipes on your system are bidirectional (as they are on Solaris 11 and some BSDs at least, but not Linux):
cmd1 <&1 | cmd2 >&0
Beware of deadlocks though.
Also note that some versions of ksh93 on some systems implement pipes (|) using a socket pair. socket pairs are bidirectional, but ksh93 explicitly shuts down the reverse direction, so the command above wouldn't work with those ksh93s even on systems where pipes (as created by the pipe(2) system call) are bidirectional.