Quote 13
PETRUCHIO
Signior Baptista, my business asketh haste,
And every day I cannot come to woo.
You knew my father well, and in him me, (2.1.121-123)
When Petruchio approaches Baptista for Kate's hand, he banks on the fact that Baptista knew his dead father. The good reputation of fathers is important to all the social climbing young men in this play. Here, however, we see that Petruchio sees his identity as being fused with that of his father, as though they are the same person.
Quote 14
PETRUCHIO
O Kate, content thee. Prithee, be not angry.
KATHERINE
I will be angry: what hast thou to do?—
Father, be quiet. He shall stay my leisure. (3.2.221-223)
This moment suggests that a daughter's relationship with her father is a good predictor of the kind of wife she will be. Kate is disrespectful to Baptista (we assume he has tried to interrupt Kate but she shuts him down before he can get a word in edgewise) and so, we can assume that she will be just as disobedient and disrespectful to her husband.
Quote 15
PETRUCHIO
Nay, I will win my wager better yet,
And show more sign of her obedience,
Her new-built virtue and obedience.
Enter Katherine, Bianca, and Widow.
See where she comes and brings your froward
wives
As prisoners to her womanly persuasion.— (5.2.129-134)
As Petruchio brags to the guys about his power to summons Kate with a simple verbal command, he simultaneously casts Katherine as one who controls other women. Here, she drags the Widow and Bianca out to center stage, where she will soon punish their insubordination to their husbands with what amounts to a verbal spanking. Kate is both imprisoned and imprisoning. (Petruchio also seems to enjoy the fact that, as Kate's husband and commander, he is capable of controlling other men's wives by proxy.)