In Act 4 Scene 2 of The Taming of the Shrew, is the merchant impersonating Vincentio a manifestation of the Induction again?

Certainly throughout The Taming of the
Shrew, as in the majority of Shakespeare's comedies, the motif of disguise,
mistaken identities, assumed identities and wilful deceit is common. What is interesting
about The Taming of the Shrew, however, is that Shakespeare gives
this play an Induction where the artificiality of such conventions is deliberately
alluded to with the theme of confused identities clearly indicated with the deception
that the Lord works on Sly to convince him that he is a Lord, a member of the
aristocracy, and then the way that his servant assumes the role of Sly's "wife." It
could be argued, therefore, that every disguise that is donned in the play acts as a
foreshadowed "echo" of the mistaken identity that has already occurred in the Induction.
The Induction in so many ways, by creating a play within a play, questions the
credibility of such disguises and comments on the audience's willingness to suspend
their disbelief and be taken in, just as Sly himself is taken in. The key difference
though is that the audience laughs at Sly and his stupidity, whereas they remain blind
to the way that they have suspended their own disbelief. As always, it is Shakespeare
that gets the last laugh.