  We show that given a rigid C*-tensor category, there is an equivalence of
categories between normalized irreducible Q-systems, also known as connected
unitary Frobenius algebra objects, and compact connected W*-algebra objects.
Although this result could be proved as a corollary of our previous article on
realizations of algebra objects and discrete subfactors, we prove it here
directly via categorical methods without passing through subfactor theory.
