If you want to know how our works participate in the atonement of Christ, there is a catechism for that as well, but it has nothing to do with purgatory (souls in purgatory cannot participate in the sacrifice of Christ because they cannot do any works; nor do they need it because they have already been saved).
Here is what the Church teaches on the unique atonement of Christ and how the living on this earth can participate in the sacrifice of Christ:
Jesus consummates his sacrifice on the cross
616 It is love "to the end"446 that confers on Christ's sacrifice its value as redemption and reparation, as atonement and satisfaction. He knew and loved us all when he offered his life.447 Now "the love of Christ controls us, because we are convinced that one has died for all; therefore all have died."448 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 surpasses and embraces all human persons, and constitutes himself as the Head of all mankind, makes possible his redemptive sacrifice for all.
617 The Council of Trent emphasizes the unique character of Christ's sacrifice as "the source of eternal salvation"449 and teaches that "his most holy Passion on the wood of the cross merited justification for us."450 and the Church venerates his cross as she sings: "Hail, O Cross, our only hope."451
Our participation in Christ's sacrifice
618 The cross is the unique sacrifice of Christ, the "one mediator between God and men".452 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.453 He calls his disciples to "take up [their] cross and follow (him)",454 for "Christ also suffered for (us), leaving (us) an example so that (we) should follow in his steps."455 In fact Jesus desires to associate with his redeeming sacrifice those who were to be its first beneficiaries.456 This is achieved supremely in the case of his mother, who was associated more intimately than any other person in the mystery of his redemptive suffering.457 Apart from the cross there is no other ladder by which we may get to heaven.458
446 ⇒ Jn 13:1.
447 Cf. ⇒ Gal 2:20; ⇒ Eph 5:2, ⇒ 25.
448 ⇒ 2 Cor 5:14.
449 ⇒ Heb 5:9.
450 Council of Trent: DS 1529.
451 LH, Lent, Holy Week, Evening Prayer, Hymn Vexilla Regis.
452 1 Tim 2:5.
453 GS 22 # 5; cf. # 2.
454 ⇒ Mt 16:24.
455 I Pt 2:21.
456 Cf ⇒ Mk 10:39; ⇒ Jn 21:18-19; ⇒ Col 1:24.
457 Cf. ⇒ Lk 2:35.
458 St. Rose of Lima: cf. P. Hansen, Vita mirabilis (Louvain, 1668).
So what is your religion, if I may ask, that is "not Protestant" yet surpisingly repeats every canard about the purgatory and atonement that the Protestans use to spread their lies?
Whether expiation means atonement or purification (I find your explanation very unsatisfying) the point remains ... your view of the atonement of Christ is lacking. Does the blood of Christ cleanse us from all sin ... or just some sin? Seems the scriptures are clear that His blood cleanses us from all sin ... there is nothing left to purify if His atonement was perfect.
If you want to know how our works participate in the atonement of Christ ...
Works do not do anything wrt salvation ... salvation is a work of God, it is absolutely free, it is not earned or deserved.
Ephesians 2:8-9
8 For by grace you have been saved through faith; and that not of yourselves, it is the gift of God;
9 not as a result of works, that no one should boast.
And ... Titus 1:9
5 He saved us, not on the basis of deeds which we have done in righteousness, but according to His mercy, by the washing of regeneration and renewing by the Holy Spirit
Hebrews 10 talks about the one sacrifice that Christ made on the cross.
10 By this will we have been sanctified through the offering of the body of Jesus Christ once for all.
11 And every priest stands daily ministering and offering time after time the same sacrifices, which can never take away sins;
12 but He, having offered one sacrifice for sins for all time, sat down at the right hand of God,
13 waiting from that time onward until His enemies be made a footstool for His feet.
14 For by one offering He has perfected for all time those who are sanctified.
If that one offering on the cross has perfected us ... where is there room for purification? What the doctrine of purgatory does is negate the clear teaching of scripture on the atonement ... and it affirms that the sacrifice of Christ did not perfect us.
When the Bible is clear on a topic ... and you desire to add something to that ... you negate the text of the scripture and follow another gospel.
So what is your religion ...
Christian ... non-denominational.
yet surpisingly repeats every canard about the purgatory and atonement that the Protestans use to spread their lies?
I have simply challenged your understanding and interpretation of 1 Cor. 3 and presented a clear passage in Hebrews 10 to clearly show that the doctrine of purgatory is unbiblical ...
My main question still stands ...
Is your faith and trust in the sacrifice of Jesus Christ ... or is it in the teaching of the RCC?