Catechism of the Catholic Church
e. Para. 618: The cross is the unique sacrifice of Christ, the "one mediator between God and men" (1 Tim 2:5). But because in his incarnate divine person he has in some way united himself to every man, "the possibility of being made partners, in a way known to God, in the paschal mystery" is offered to all men (GS 22 § 5; cf. § 2).
Para. 611: The Eucharist that Christ institutes at that moment will be the memorial of his sacrifice (1 Cor 11:25). Jesus includes the apostles in his own offering and bids them perpetuate it (Cf. Lk 22:19). By doing so, the Lord institutes his apostles as priests of the New Covenant: "For their sakes I sanctify myself, so that they also may be sanctified in truth" (Jn 17:19; cf. Council of Trent: DS 1752; 1764).
Para. 616: . . . No man, not even the holiest, was ever able to take on himself the sins of all men and offer himself as a sacrifice for all. The existence in Christ of the divine person of the Son, who at once surpassses and embraces all human persons and constitutes himself as the Head of all mankind, makes possible his redemptive sacrifice for all.
Para. 612: The cup of the New Covenant, which Jesus anticipated when he offered himself at the Last Supper, is afterwards accepted by him from his Father's hands in his agony in the garden at Gethsemani (Cf. Mt 26:42; Lk 22:20), making himself "obedient unto death." Jesus prays: "My Father, if it be possible, let this cup pass from me. . . ." (Phil 2:8; Mt 26:39; cf. Heb 5:7-8). Thus he expresses the horror that death represented for his human nature.