"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 [...]
“The sacrifice of Christ and the sacrifice of the Eucharist are one single sacrifice: ‘The victim is one and the same: the same now offers through the ministry of priests, who then offered himself on the cross; only the manner of offering is different.’ ‘In this divine sacrifice which is celebrated in the Mass, the [...]
"The Eucharist is thus a sacrifice because it re-presents (makes present) the sacrifice of the cross, because it is its memorial and because it applies its fruit: [Christ], our Lord and God, was once and for all to offer himself to God the Father by his death on the altar of the cross, to accomplish [...]
"Because it is the memorial of Christ's Passover, the Eucharist is also a sacrifice. the sacrificial character of the Eucharist is manifested in the very words of institution: 'This is my body which is given for you' and 'This cup which is poured out for you is the New Covenant in my blood.' In the [...]
"In the New Testament, the memorial takes on new meaning. When the Church celebrates the Eucharist, she commemorates Christ's Passover, and it is made present the sacrifice Christ offered once for all on the cross remains ever present. "As often as the sacrifice of the Cross by which 'Christ our Pasch has been sacrificed' is [...]
"In the sense of Sacred Scripture the memorial is not merely the recollection of past events but the proclamation of the mighty works wrought by God for men. In the liturgical celebration of these events, they become in a certain way present and real. This is how Israel understands its liberation from Egypt: every time [...]
"The Eucharist is also the sacrifice of praise by which the Church sings the glory of God in the name of all creation. This sacrifice of praise is possible only through Christ: he unites the faithful to his person, to his praise, and to his intercession, so that the sacrifice of praise to the Father [...]
"The Eucharist is a sacrifice of thanksgiving to the Father, a blessing by which the Church expresses her gratitude to God for all his benefits, for all that he has accomplished through creation, redemption, and sanctification. Eucharist means first of all 'thanksgiving.'" Source: Catechism of the Catholic Church #1360
"The Eucharist, the sacrament of our salvation accomplished by Christ on the cross, is also a sacrifice of praise in thanksgiving for the work of creation. In the Eucharistic sacrifice the whole of creation loved by God is presented to the Father through the death and the Resurrection of Christ. Through Christ the Church can [...]
"We must therefore consider the Eucharist as: thanksgiving and praise to the Father; the sacrificial memorial of Christ and his Body; the presence of Christ by the power of his word and of his Spirit." Source: Catechism of the Catholic Church #1358