John Chrysostom

"The cloak that I left at Troas with Carpus, when thou comest bring with thee, and the books, but especially the parchments." The word here translated "cloak" may mean a garment, or, as some say, a bag, in which the books were contained. But what had he to do with books, who was about to depart and go to God? He needed them much, that he might deposit them in the hands of the faithful, who would retain them in place of his own teaching.

Homily on 2 Timothy 10 ↗

Theophylact of Ohrid

Here the apostle speaks of the cloak; he asks for it so as not to have need to take from others. For everywhere he takes great care not to be in need of others. Some, however, think that this is a case, a container in which the books were kept. Why did he need books when he was preparing to depart to God? So that he might pass them on to the faithful, that they might have them in his stead. Probably, they contained within themselves something more valuable.

Commentary on 2 Timothy ↗

Thomas Aquinas

Then when he says, "the cloak that I left at Troas with Carpus," he tells him what to carry. Carpus is a saint. According to Jerome, the cloak, or penula, was a volume of the law which he kept on a scroll. Or a penula was an article of clothing; but according to Chrysostom, it was a common article of clothing. And because the Apostle lived as a poor man in Rome, he wanted his clothes brought to him. …

Commentary on 2 Timothy ↗