Triumph - Vine's Expository Dictionary of New Testament Words
Triumph[ 1,,G2358, thriambeuo ]
(a) to lead in triumph," used of a conqueror with reference to the vanquished, 2 Corinthians 2:14. Theodoret paraphrases it "He leads us about here and there and displays us to all the world." This is in agreement with evidences from various sources. Those who are led are not captives exposed to humiliation, but are displayed as the glory and devoted subjects of Him who leads (See the context). This is so even if there is a reference to a Roman "triumph." On such occasions the general's sons, with various officers, rode behind his chariot (Livy, xlv. 40). But there is no necessary reference here to a Roman "triumph" (Field, in Notes on the Trans. of the NT). The main thought is that of the display, "in Christ" being the sphere; its evidences are the effects of gospel testimony.
In Colossians 2:15 the circumstances and subjects are quite different, and relate to Christ's victory over spiritual foes at the time of His death; accordingly the reference may be to the triumphant display of the defeated.