What follows is from a very old (but still very useful) commentary and a few ideas expressed here are no longer considered as tenable by most scholars. I will add footnotes of my own to the text on Tuesday or Wednesday(These will be in bold-face italics, like this notice). The translated text I’m linking to is not the same as that used by Lapide.
1 Corinthians 1:1 Sosthenes was chief ruler of the synagogue at Corinth; having been converted to Christ by Paul, he was severely beaten for his faith before Gallio, the Proconsul (Acts 18:17), and after his death was placed among the Saints-November 28th. The identification between the Sosthenes of Acts and the person named here is probably certain, though St Luke does not describe Sosthenes as a Christian but, given the treatment he receives in Acts, it is highly likely that he was converted by St Paul.
1 Corinthians 1:2 Unto the church of God which is at Corinth, to them that are sanctified in Christ Jesus, called to be saints, grace be unto you and peace from God. For called to be saints the Syriac translates, called and saints. But the Greek is kletos, a word which gives the meaning having a call to holiness, or holy by way of a cause, called to holiness. The adjective is used in this letter only in 1:1 of Paul, here in vs 2 of the Corinthians, and in verse 24 of Christians in general. The verb “kaleo” (to call) or its derivatives is used 12 times in the letter, highlighting it as an important theme.
Note first, that Paul throughout this chapter and everywhere else holds up to admiration this benefit of calling. Secondly, that this and all other benefits be humbly and devoutly ascribed to the Divine benevolence and to the power of humility. Chrysostom has here a noteworthy passage in the moral part of his first homily. You can read what Chrysostom has to say here, in sections 4-6.
Thirdly, it is plain from this, in opposition to Pelagius, that, not for our merits, but by the mere grace of God, have we been called to the faith and the grace of Christ. Note that all Christians were formerly called Saints: not because they were really so, but by way of call, profession, duty. Concerning the necessity of grace see HERE. Concerning the words “all Christians were formerly called saints:” in Lapide’s day, like our own, the term saint was seldom applied to Christians living in this world, the underlying concept however was, and has always been retained (see HERE).
Fourthly, he calls them saints in Christ, that is sanctified through the merits of Christ, namely, in Baptism and its consequent gifts. Concerning the gifts received at Baptism see HERE. See also the index of the Catechism under the heading “Baptism” (sub-heading “effects”).
Fifthly: “the church,” and the “called to be saints” are the same thing. For the latter is in apposition and is explanatory of the former: so that if you ask, What is the Church? I shall answer from this passage of St Paul: It consists of those called to be Saints, or it is a congregation and assembly of the faithful, who have been called to holiness. Our word Church commonly translates the Greek word ekklesia, which is derived from ekkalein, meaning to call someone out. Ekklesia refers to those who have been called out, hence a congregation or assembly. Ekklesia and ekkalein are related to the words kletos and kaleo referred to earlier.
Whence, sixthly, it is evident from here that the Church is visible; for Paul writes these things not to an abstract idea, but “to the church which is at Corinth,” which was able to read and see his letters, as is plain.
Seventhly, from this place it is evident that there is the same Church everywhere, a part of which was the Church at Corinth. Whence he says: “With all that in every place call upon the name of Jesus Christ our Lord, both theirs and ours;” i.e., all Christians, wherever they exist; whether with me in this place of ours, or in any other place you please. Theirs, then, is said of the Corinthians, and ours of Paul and Sosthenes. He adds this, that no one might suppose when he said Jesus Christ our Lord, that he meant to say that Christ is the Lord of Paul and Sosthenes alone. So Chrysostom says: “By this Paul tacitly enjoins the Corinthians that they ought to lay aside contention and to be of one mind, as being members of the same Church, and of the same Head, Christ.” Next, he reminds them that he writes this letter specially indeed to the Corinthians, but, nevertheless, that he wishes it to be a circular letter to all Christians, in the same way that the letters of the other Apostles and of the Bishops in those first ages were circular letters. To say that a part of the Church was at Corinthis to give an incorrect formulation. Concerning this, see HERE.
Cajetan’s interpretation of ours, that it means, “Our jurisdiction extends itself to Corinth and to the Corinthians, so that the city and district of Corinth is both theirs and ours,” is forced.
1 Corinthians 1:4 I thank my God always on your behalf, for the grace of God which is given you by Jesus Christ. “For the grace” means in the Greek: “on account of the grace of God” which is given you in Christ, i.e., through Christ. “The source,” says St Bernard, “of all the springs and rivers is the sea: but the source of all virtue and knowledge is the Lord Jesus Christ: the continence of the flesh, the energy of the heart, the rectitude of the will, all flow from that spring: let the heavenly stream be given back to its source” (by thanksgiving), “so that the faintest parts of the earth may be replenished; ‘I will not give my glory to another’ saith the God’” (Isaiah 48:11).
1 Corinthians 1:5 That in everything ye are enriched by Him (by Christ), in all utterance (of the preaching of the Gospel), and in all knowledge, that is, in spiritual understanding of Him. In other words, I give thanks to God, because by me and Apollos He put before you, richly, the preaching and doctrine of the Gospel and a perception and understanding of it. Certainly the preaching of the gospel brings enrichment and knowledge, most scholars would probably disagree with that ideas application here. “Utterance” (word, discourse) and “knowledge” are charismatic gifts which the Corinthians has received (see 1 Corinthians 13:1-2; 2 Corinthians 8:7).
1 Corinthian 1:6 Even as the testimony of Christ was confirmed in you-i.e., by which, as by two testimonies, the Christian faith was founded and established in you. Some translate through which the testimony…i.e., through knowledge and understanding the testimony of Christ was confirmed among you. Others interpret, Even as the testimony…thus: by which things (knowledge and understanding) it is known that you are faithful and disciples of Christ. In light of what I wrote immediately above, the confirmation of the testimony is the spiritual gifts they have received. For some of the gifts Paul has in mind, see 1 Corinthians 12:1-11.
1 Corinthians 1:7 Waiting for the coming of our Lord Jesus Christ, in His second Advent, when you will receive from Christ an abundant supply of all graces, and your consummation in heavenly glory.
1 Corinthians 1:8 Who shall also confirm you, so far as His part is: i.e., shall give grace which can confirm you, and shall confirm you indeed, if you are willing to receive it, to use it, and to confirm yourselves in the faith and love of Christ: shall confirm you, I say, for this, that ye may be, and may preserve unto the end (of life) blameless; that is, unaccused, whom no one can charge with having committed anything against the faith and love of Christ. The Apostle speaks to the whole Church, in which the greater number were holy and blameless, although some few were sowing schisms, and these in the following verse he reproves and condemns.
In the day of our Lord Jesus Christ. It is an ellipse common with the Apostle: for we must supply, that ye may be and may appear, blameless in that day of the advent and judgment of Christ.
1 Corinthians 1:9 God is faithful, by whom ye were called unto the fellowship of His Son Jesus Christ our Lord. Note, faithful with St Paul is the same as constant, truthful, as I shall show on 1 Timothy 1:15; not, according to Calvin, as though God saves those only who have been effectually called by Him, and all of them; and as though He bids and makes each one of them believe with a firm faith that he will be saved. For if so, why in the next verse, anxious about the salvation of the Corinthians, does he condemn their divisions? Had not the Corinthians believed?-and yet, having lapsed into schisms, they had incurred the danger of damnation, and, therefore, can lapse into sin and be damned. God, then, is said to be faithful, because, not without cause, will He, O Corinthians, withdraw His help from you which He began to give, and afterwards promised that He would give, in order that you might persevere and be confirmed in the faith and fellowship of Jesus; nor will He desert you unless He be first deserted by you; as the Council of Trent teaches (following St Augustine), Sess.VI c. 11 and 13, where it lays down the same three things which the Apostles does here: (1) That God gives the grace of Christ to all the justified: because , if they are willing, they are able to persevere in righteousness. (2) That by their own will they can fall from it. (3) that no one knows whether he will persevere, and whether he is of the number of the elect, unless he has a special revelation of it from God.
Note secondly. Paul here calls the communion of the faith, grace and glory of Christ which is enjoyed in the Church of Christ, the fellowship of the Son; or that partaking of Christ in which we have a fellowship of sonship, inheritance, the Sacraments, and all the benefits of Christ. In other words: Ye are called to be sons of God, fellows, members, brothers, and co-heirs of Christ: so Anselm, Ambrose, Theophylact and Chrysostom, and 1 John 1:3. And here notice: although, as the Apostle says, all faithful Christians are of the fellowship of Christ, yet some are more so than others: that is to say, those who share more largely of the life and grace of Christ: as those who follow, not only the precepts, but also the counsels of Christ. We are all to progress and grow in holiness.