Whether Christ's cross should be worshipped with the adoration of "latria"?

Objections

Objection 1 : It would seem that Christ's cross should not be worshiped with the adoration of "latria." For no dutiful son honors that which dishonors his father, as the scourge with which he was scourged, or the gibbet on which he was hanged; rather does he abhor it. Now Christ underwent the most shameful death on the cross; according to Wis. 2:20: "Let us condemn Him to a most shameful death." Therefore we should not venerate the cross but rather we should abhor it.
Objection 2 : Further, Christ's humanity is worshiped with the adoration of "latria," inasmuch as it is united to the Son of God in Person. But this cannot be said of the cross. Therefore Christ's cross should not be worshiped with the adoration of "latria."
Objection 3 : Further, as Christ's cross was the instrument of His passion and death, so were also many other things, for instance, the nails, the crown, the lance; yet to these we do not show the worship of "latria." It seems, therefore, that Christ's cross should not be worshiped with the adoration of "latria."