Today’s Catechism sections discuss the sacrifice of the Eucharist. Supporting material comes from St. Augustine’s “City of God”.

1368 The Eucharist is also the sacrifice of the Church. The Church which is the Body of Christ participates in the offering of her Head. With him, she herself is offered whole and entire. She unites herself to his intercession with the Father for all men. In the Eucharist the sacrifice of Christ becomes also the sacrifice of the members of his Body. The lives of the faithful, their praise, sufferings, prayer, and work, are united with those of Christ and with his total offering, and so acquire a new value. Christ's sacrifice present on the altar makes it possible for all generations of Christians to be united with his offering.

In the catacombs the Church is often represented as a woman in prayer, arms outstretched in the praying position. Like Christ who stretched out his arms on the cross, through him, with him, and in him, she offers herself and intercedes for all men.

1369 The whole Church is united with the offering and intercession of Christ. Since he has the ministry of Peter in the Church, the Pope is associated with every celebration of the Eucharist, wherein he is named as the sign and servant of the unity of the universal Church. The bishop of the place is always responsible for the Eucharist, even when a priest presides; the bishop's name is mentioned to signify his presidency over the particular Church, in the midst of his presbyterium and with the assistance of deacons. The community intercedes also for all ministers who, for it and with it, offer the Eucharistic sacrifice:

Let only that Eucharist be regarded as legitimate, which is celebrated under [the presidency of] the bishop or him to whom he has entrusted it.189

Through the ministry of priests the spiritual sacrifice of the faithful is completed in union with the sacrifice of Christ the only Mediator, which in the Eucharist is offered through the priests' hands in the name of the whole Church in an unbloody and sacramental manner until the Lord himself comes.190

1370 To the offering of Christ are united not only the members still here on earth, but also those already in the glory of heaven. In communion with and commemorating the Blessed Virgin Mary and all the saints, the Church offers the Eucharistic sacrifice. In the Eucharist the Church is as it were at the foot of the cross with Mary, united with the offering and intercession of Christ.

1371 The Eucharistic sacrifice is also offered for the faithful departed who "have died in Christ but are not yet wholly purified,"191 so that they may be able to enter into the light and peace of Christ:

Put this body anywhere! Don't trouble yourselves about it! I simply ask you to remember me at the Lord's altar wherever you are.192

Then, we pray [in the anaphora] for the holy fathers and bishops who have fallen asleep, and in general for all who have fallen asleep before us, in the belief that it is a great benefit to the souls on whose behalf the supplication is offered, while the holy and tremendous Victim is present.... By offering to God our supplications for those who have fallen asleep, if they have sinned, we . . . offer Christ sacrificed for the sins of all, and so render favorable, for them and for us, the God who loves man.193

1372 St. Augustine admirably summed up this doctrine that moves us to an ever more complete participation in our Redeemer's sacrifice which we celebrate in the Eucharist:

This wholly redeemed city, the assembly and society of the saints, is offered to God as a universal sacrifice by the high priest who in the form of a slave went so far as to offer himself for us in his Passion, to make us the Body of so great a head.... Such is the sacrifice of Christians: "we who are many are one Body in Christ" the Church continues to reproduce this sacrifice in the sacrament of the altar so well-known to believers wherein it is evident to them that in what she offers she herself is offered.194

St. Augustine explains true sacrifice in “City of God” (10, 6)

Chapter 6 - Of the True and Perfect Sacrifice.

Thus a true sacrifice is every work which is done that we may be united to God in holy fellowship, and which has a reference to that supreme good and end in which alone we can be truly blessed. And therefore even the mercy we show to men, if it is not shown for God's sake, is not a sacrifice. For, though made or offered by man, sacrifice is a divine thing, as those who called it sacrifice meant to indicate. Thus man himself, consecrated in the name of God, and vowed to God, is a sacrifice in so far as he dies to the world that he may live to God. For this is a part of that mercy which each man shows to himself; as it is written, Have mercy on your soul by pleasing God. Sirach 30:24 Our body, too, as a sacrifice when we chasten it by temperance, if we do so as we ought, for God's sake, that we may not yield our members instruments of unrighteousness unto sin, but instruments of righteousness unto God. Romans 6:13 Exhorting to this sacrifice, the apostle says, I beseech you, therefore, brethren, by the mercy of God, that you present your bodies a living sacrifice, holy, acceptable to God, which is your reasonable service. Romans 12:1 If, then, the body, which, being inferior, the soul uses as a servant or instrument, is a sacrifice when it is used rightly, and with reference to God, how much more does the soul itself become a sacrifice when it offers itself to God, in order that, being inflamed by the fire of His love, it may receive of His beauty and become pleasing to Him, losing the shape of earthly desire, and being remoulded in the image of permanent loveliness? And this, indeed, the apostle subjoins, saying, And be not conformed to this world; but be transformed in the renewing of your mind, that you may prove what is that good, and acceptable, and perfect will of God. Romans 12:2 Since, therefore, true sacrifices are works of mercy to ourselves or others, done with a reference to God, and since works of mercy have no other object than the relief of distress or the conferring of happiness, and since there is no happiness apart from that good of which it is said, It is good for me to be very near to God, it follows that the whole redeemed city, that is to say, the congregation or community of the saints, is offered to God as our sacrifice through the great High Priest, who offered Himself to God in His passion for us, that we might be members of this glorious head, according to the form of a servant. For it was this form He offered, in this He was offered, because it is according to it He is Mediator, in this He is our Priest, in this the Sacrifice. Accordingly, when the apostle had exhorted us to present our bodies a living sacrifice, holy, acceptable to God, our reasonable service, and not to be conformed to the world, but to be transformed in the renewing of our mind, that we might prove what is that good, and acceptable, and perfect will of God, that is to say, the true sacrifice of ourselves, he says, For I say, through the grace of God which is given unto me, to every man that is among you, not to think of himself more highly than he ought to think, but to think soberly, according as God has dealt to every man the measure of faith. For, as we have many members in one body, and all members have not the same office, so we, being many, are one body in Christ, and every one members one of another, having gifts differing according to the grace that is given to us. Romans 12:3-6 This is the sacrifice of Christians: we, being many, are one body in Christ. And this also is the sacrifice which the Church continually celebrates in the sacrament of the altar, known to the faithful, in which she teaches that she herself is offered in the offering she makes to God.

Footnotes

189 St. Ignatius of Antioch, Ad Smyrn. 8:1; SCh 10, 138.
190 PO 2 # 4.
191 Council of Trent (1562) DS 1743.
192 St. Monica, before her death, to her sons, St. Augustine and his brother; Conf. 9, 11, 27: PL 32, 775.
193 St. Cyril of Jerusalem, Catech. myst. 5, 9. 10 PG 33, 1116-1117.
194 St. Augustine, De civ Dei, 10, 6: PL 41, 283; cf. ⇒ Rom 12:5.