This section of Chapter 4 has seven verses:

2 Timothy 4:9-15
9 Do thy diligence to come shortly unto me:
10 For Demas hath forsaken me, having loved this present world, and is departed unto Thessalonica; Crescens to Galatia, Titus unto Dalmatia.
11 Only Luke is with me. Take Mark, and bring him with thee: for he is profitable to me for the ministry.
12 And Tychicus have I sent to Ephesus.
13 The cloke that I left at Troas with Carpus, when thou comest, bring with thee, and the books, but especially the parchments.
14 Alexander the coppersmith did me much evil: the Lord reward him according to his works:
15 Of whom be thou ware also; for he hath greatly withstood our words.

We will begin with the Barclay commentary:

A ROLL OF HONOUR AND DISHONOUR

PAUL draws up a roll of honour and of dishonour of his friends.  Some are only names to us; of some, as we read the Acts of the Apostles as well as the Epistles, we get the occasional revealing glimpse. If we are allowed to use our imagination, we can reconstruct some of the stories. ~Barclay commentary

Now to the rest of the commentaries. We will begin with the general and go to the specific.

First the Matthew Henry breaking into the commentary on verses 9-15 where it begins discussing verse 13:

Paul orders Timothy to come to him, bids him as he came through Troas to bring with him thence those things which he had left behind him there (2 Timothy 4:13), the cloak he had left there, which, it may be, Paul had the more occasion for in a cold prison. It is probable that it was the habit Paul usually wore, a plain dress. Some read it, the roll of parchment I left at Troas; others, the desk that I left. Paul was guided by divine inspiration, and yet he would have his books with him. Whereas he had exhorted Timothy to give attendance to reading, so he did himself, though he was now ready to be offered. As long as we live, we must be still learning. But especially the parchments, which some think were the originals of his epistles; others think they were the skins of which he made his tents, whereby he obtained a livelihood, working with his own hands. ~Matthew Henry Main

Now the Matthew Henry Concise:

The love of this world, is often the cause of turning back from the truths and ways of Jesus Christ. Paul was guided by Divine inspiration, yet he would have his books. As long as we live, we must still learn. The apostles did not neglect human means, in seeking the necessaries of life, or their own instruction. Let us thank the Divine goodness in having given us so many writings of wise and pious men in all ages; and let us seek that by reading them our profiting may appear to all. ~Matthew Henry Concise.

Now something from the Biblical Illustrator:

Paul—his cloak and his books
I. Let us look at this memorable cloak which Paul left with Carpus at Troas. Troas was a principal seaport-town of Asia Minor. Very likely the apostle Paul was seized at Troas on the second occasion of his being taken before the Roman emperor. The soldiers usually appropriated to themselves any extra garment in the possession of an arrested person, such things being considered as the perquisites of those who made the arrest. The apostle may have been forewarned of his seizure, and therefore prudently committed his few books and his outer garment, which made up all his household stuff, to the care of a certain honest man named Carpus. Although Troas was full six hundred miles’ journey from Rome, yet the apostle Paul is too poor to purchase a garment, and so directs Timothy, as he is coming that way, to bring his cloak. He needs it much, for the sharp winter is coming on, and the dungeon is very, very chilly.

1. Let us perceive here with admiration, the complete self-sacrifice of the apostle Paul for the Lord’s sake. Remember what the apostle once was. He was great, famous, and wealthy. Ah! how he emptied himself, and to what extremity of destitution was he willing to bring himself for Christ’s name sake. The Saviour must die in absolute nakedness, and the apostle is made something like Him as he sits shivering in the cold.

2. We learn how utterly forsaken the apostle was by his friends. If he had not a cloak of his own, could not some of them lend him one? No; he is so utterly left, that although he is ready to die of ague in the dungeon, not a soul will lend or give him a cloak. What patience does this teach to those similarly situated I In your greatest trials do you find your fewest friends? Have those who once loved and respected you fallen asleep in Jesus? And have others turned out to be hypocritical and untrue? “Notwithstanding the Lord stood with me, and strengthened me.” So now, when man deserts you, God will be your Friend.

3. Our text shows the apostle’s independence of mind. Why did not he borrow a cloak? Why did not he beg one? That is not the apostle’s taste at all. He has a cloak, and though it is six hundred miles away, he will wait until it comes. A Christian man would do well to remember that it is never to his honour, though it is not always to his dishonour, to beg.

4. We see here, how very little the apostles thought of how they were dressed. Paul wants enough to keep him warm; he asks no more. When good Bishop Hooper was led out to be burnt, he had been long in prison, and his clothes were so gone from him, that he borrowed an old scholar’s gown, full of rags and holes, that he might put it on, and went limping with pains of sciatica and rheumatism to the stake. We read of Jerome of Prague, that he lay in a damp, cold dungeon, and was refused anything to cover him in his nakedness and cold. Every saint is an image of Christ, but a poor saint is His express image, for Christ was poor. So, if you are brought to such a pitch with regard to poverty, that you scarcely know how to provide things decent by way of raiment, do not be dispirited; but say, “My Master suffered the same, and so did the apostle Paul”; and so take heart, and be of good cheer.

5. Paul’s cloak at Troas shows me how mighty the apostle was to resist temptation. “I do not see that,” you say. The apostle had the gift of miracles. Our Saviour, though able to work miracles, never wrought anything like a miracle on His own account; nor did His apostles. Miraculous gifts were entrusted to them with gospel ends and purposes, for the good of others, and for the promotion of the truth; but never for themselves.

II. We will look at his books. We do not know what the books were about, and we can only form some guess as to what the parchments were. Paul had a few books which were left, perhaps wrapped up in the cloak, and Timothy was to be careful to bring them.

1. Even an apostle must read. He is inspired, and yet he wants books! He has been preaching at least for thirty years, and yet he wants books! He had seen the Lord, and yes he wants books! He had had a wider experience than most men, and yet he wants books! He had been caught up into the third heaven, and had heard things which it was unlawful for a man to utter, yet he wants books! He had written the major part of the New Testament, and yet he wants books! The apostle says to Timothy, and so he says to every preacher, “Give thyself unto reading.” The man who never reads will never be read; he who never quotes will never be quoted, lie who will not use the thoughts of other men’s brains proves that he has no brains of his own.

2. Paul herein is a picture of industry. He is in prison; he cannot preach: what will he do? As he cannot preach, he will read. As we read of the fishermen of old and their boats. The fishermen were gone out of them. What were they doing? Mending their nets. So if Providence has laid you upon a sick bed, and you cannot teach your class—if you cannot be working for God in public, mend your nets by reading. If one occupation is taken from you, take another, and let the books of the apostle read you a lesson of industry.

III. We now want to have an interview with the apostle Paul himself, for we may learn much from him. The poor old man, without his cloak, wraps his ragged garment about him. Sometimes you see him kneeling down to pray, and then he dips his pen into the ink, and writes to his dear son Timothy. No companion, except Luke, who occasionally comes in for a short time. Now, how shall we find the old man? What sort of temper will he be in?

1. We find him full of confidence in the religion which has cost him so much.
2. But he is not only confident. You will notice that this grand old man is having communion with Jesus Christ in his sufferings.
3. Triumphant.
4. In expectation of a crown. ~The Biblical Illustrator

Here is another item from the Biblical Illustrator

A good book a lasting companion
Truths which it has taken years to glean are therein at once freely but carefully communicated. We enjoy communion with the mind, though not with the person of the writer. Thus the humblest man may surround himself by the wisest and best spirits of past and present ages. No one can be solitary who possesses a book; he owns a friend that will instruct him in moments of leisure or of necessity. It is only necessary to turn over the leaves, and the fountain at once gives forth its streams. You may seek costly furniture for your homes, fanciful ornaments for your mantelpieces, and rich carpets for your floors; but, after the absolute necessaries for a home give me books as at once the cheapest, and certainly the most useful and abiding embellishments. ~The Biblical Illustrator

Now to the specific commentaries

This verse is broken out in four parts:

1] The cloke that I left at Troas with Carpus.
2] When thou comest, bring with thee.
3] And the books.
4] But especially the parchments.

1] The cloke that I left at Troas with Carpus.
The cloak that I left at Troas with Carpus - About the word here rendered a "cloak", interpreters are not agreed: some take it for a garment, and about this they differ; some would have it to be a dignified robe, such as the Roman consuls and senators of Rome wore; which is not likely, this being not suitable to the apostle's character, state, and circumstances. Others take it to be a courser and meaner garment, wore in cold and rainy weather, to preserve from the [inclemencies—severe, rough, stormy] of it; and winter now coming on, 2 Timothy 4:21 the apostle sends for it; which he perhaps had left at Troas in the summer season, as he came: but others take it to be a kind of desk or scrutoire [skroo-twahr-writing desk] , to put papers in, or a chest for books, a book press; and so the Syriac [seer-ee-ak] version renders it; and which agrees with what follows. Jerom understands it of a book itself, of the Hebrew volume of the Pentateuch [pen-tuh-took]. Troas, where this cloak, or book press, or book was, was a city in Asia Minor, that stood upon, or near the same place where old Troy stood, and from whence it seems to have had its name, and lay in Timothy's way from Ephesus to Rome; See Gill on Acts 16:8, Acts 20:7 and as for Carpus, he was Paul's host when he was at Troas. Some make him to be first bishop of Laodicea, and then of Crete; he is reckoned among the seventy disciples, and is said to be bishop of Berytus in Thrace; See Gill on Luke 10:1. ~John Gill

Quoted verses:
2 Timothy 4:21 [see Lesson]
Do thy diligence to come before winter. Eubulus greeteth thee, and Pudens, and Linus, and Claudia, and all the brethren.

Acts 16:8
And they passing by Mysia came down to Troas.

Acts 20:7
And upon the first day of the week, when the disciples came together to break bread, Paul preached unto them, ready to depart on the morrow; and continued his speech until midnight.

Luke 10:1
After these things the Lord appointed other seventy also, and sent them two and two before his face into every city and place, whither he himself would come.

2] When thou comest, bring with thee.
When thou comest, bring with thee - he would have him call for it at Troas as he came by, and bring it with him: ~John Gill

3] And the books.
And the books - that were in it, or were there, besides the Hebrew Pentateuch: the apostle was a great reader of books, of various sorts, both Gentile and Jewish, as appears by his citations out of the Heathen poets, and his acquaintance with Jewish records, Acts 17:28. And though he was now grown old, and near his exit, yet was mindful and careful of his books, and desirous of having them to read; and herein set an example to Timothy and others, and enforced the exhortation he gave him, 1 Timothy 4:13. ~John Gill

Quoted verses:
Acts 17:28
For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring.

1 Timothy 4:13 [see Lesson]
Till I come, give attendance to reading, to exhortation, to doctrine.

4] But especially the parchments.
But especially the parchments: which might contain his own writings he had a mind to revise before his death, and commit into the hands of proper persons; or some observations which he had made in his travels, concerning persons and things; though it is most likely that these were the books of the Old Testament, which were written on parchments, and rolled up together; and hence they are called the volume of the book; and these the apostle had a special regard for, that whatever was neglected, he desired that these might not, but be carefully brought unto him. ~John Gill