SCHISM
The Code of Canon Law gives us the official definition of Schism: if, finally, he refuses to be subject to the Supreme Pontiff, or to have communication with the members of the church subject to the Pope, he is a schismatic. (Canon 1325) It is also recommended to visit the section on heresy, especially the sin of communicatio in sacris.Subject to the Roman Pontiff
Indeed we declare, say, pronounce, and define that it is altogether necessary to salvation for every human creature to be subject to the Roman Pontiff. (Pope Boniface VII in the infallible Bull, Unam sanctam) It is the duty of all Catholics to be subject to the lawful pastors of the Church, that is to the Pope and those who are sent by the Pope. But the Episcopal order is rightly judged to be in communion with Peter, as Christ commanded, if it be subject to and obeys Peter; otherwise it necessarily becomes a lawless and disorderly crowd., Satis Cognitum of Pope Leo XIII. Bishops first and foremost must be subject to the Roman Pontiff. And they govern their diocese in subjection to the Pope. The Pastors of the parishes govern in subjection to their Ordinary (Diocesan Bishop) and to the Pope, both of whom they mention daily in the Canon of the Mass. The faithful in turn obey the Pope, their Ordinary and their Pastor. (In missionary territories a slightly different arrangement exists, but the men claiming obedience can trace their authority through their superior(s) back to the Pope.) To adhere to a false Bishop of Rome [a false "pope"] is to be out of communion with the Church. -St. Cyprian. To adhere to an Antipope is to be in schism from the true Pope. It is also schismatic to refuse to adhere to any Bishop of Rome. This is why the Orthodox are considered schismatic in that they refuse obedience to the Pope altogether. The sede vacantists are also schismatic in that they proclaim that there is no Pope and act as if there will never be a Pope again. This denies the infallible doctrine of the only Vatican Council (DZ 1825): If anyone then says that it is not from the institution of Christ the Lord Himself, or by divine right that the blessed Peter has perpetual successors in the primacy over the universal Church, or that the Roman Pontiff is not the successor of the blessed Peter in the same primacy, let him be anathema.In conclusion we must hold as schismatics all those who adhere to any of hte Antipoeps, especially to Antipope Benedict XVI, since it is obvious that he has not been a member of the Church for decades and therefore as Saint Robert Bellarmine (among others) observes, cannot be head of the Catholic Church. We must also hold as schismatic those with false ideas of the Papacy, such as the material formal crowd and the sede vacantists. In the former case they hold that a heretic can retain some claim to the Papacy and when he converts obtains full authority. The latter, as stated above, hold in practice that there will neer be a Pope again for they have made no effort to end the vacancy they proclaim exists. Pope Leo XIII in Satis Cognitum states: Heresies and schisms have no other origin than that obedience is refused to the priest of God, and that men lose sight of the fact that there is one judge in the place of Christ in this world" (Epist. xii. ad Cornelium, n. 5). No one, therefore, unless in communion with Peter can share in his authority, since it is absurd to imagine that he who is outside can command in the Church. Wherefore Optatus of Milevis blamed the Donatists for this reason: "Against which ages (of hell) we read that Peter received the saving keys, that is to say, our prince, to whom it was said by Christ: 'To thee will I give the keys of the Kingdom of Heaven, and the gates of hell shall not conquer them.' Whence is it therefore that you strive to obtain for yourselves the keys of the Kingdom of Heaven—you who fight against the chair of Peter?"Communion With Those Subject to the Roman Pontiff
That there might be no schism in the body: but the members might be mutually careful one for another. (I Corinthians 12:25)Now I beseech you, brethren, by the name of our Lord Jesus Christ, that you all speak the same thing and that there be no schisms among you: but that you be perfect in the same mind and in the same judgment. For it hath been signified unto me, my brethren, of you, by them that are of the house of Chloe, that there are contentions among you. Now this I say, that every one of you saith: I indeed am of Paul; and I am of Apollo; and I of Cephas; and I of Christ. Is Christ divided? Was Paul then crucified for you? Or were you baptized in the name of Paul? (I Corinthians 1:10-13)Therefore, whilst we have time, let us work good to all men, but especially to those who are of the household of the faith. (Galatians 6:10)Notice Saint Paul calls us the household (singular) of the faith. Our unity is not only with the Roman Pontiff and our lawful pastors unerneath him, but with each other as members of the household of the faith. In Galatians (5:20) Saint Paul numbers sects and dissensions as works of the flesh to be avoided. Cardinal Manning comments: At first sight some may wonder why St. Paul after summing up a black list of the sins of the flesh adds “enmities, contentions, emulations, wraths, quarrels, dissensions, sects,” and closes with “murders, drunkenness, revellings, and suchlike.” (Galatians 5:19-21) In truth, the spiritual sins of “enmities and dissensions” are more Satanic than the sins of the flesh, for Satan has no body; and they are more at variance with God, because they are spiritual, and God is charity. Saint Augustine De Fide et Symbolo, 21:We believe, too, in Holy Church, assuredly the Catholic Church. For heretics and schismatics call their assemblies ‘churches’. But heretics, since they hold false ideas of God, violate the faith itself, while schismatics, although believing what we do, have by their wicked divisions broken away from fraternal charity. Heretics, then, do not belong to the Catholic Church-for it loves God; nor do schismatics-for the Church loves its neighbor.Schism in all of its forms is uncharitable a sin against charity. Now charity is the love of God and the love of our neighbor FOR THE LOVE OF GOD and in union with His most holy will for our neighbor. I Peter 4:8: But before all things have a constant mutual charity among yourselves: for charity covereth a multitude of sins. Effects of Schism
For not every sin, however great it may be, is such as of its own nature to sever a man from the Body of the Church, as does schism or heresy or apostasy. (Pope Pius XII, Mystici Corporis Christi) This is in accord with the infallible Bull Cum Ex Apostolatus Officio, which states that schismatics canot be promoted in the Catholic Church to higher offices and Canon 188, paragraph 4 which states that they resign all offices in the Church and the Church accepts the resignation without any need of further declaration. As a logical consequence of departing from the Catholic Church, Saint Thomas states (Summa II-II Q39 A3): On the other hand, the power of jurisdiction is that which is conferred by a mere human appointment. Such a power as this does not adhere to the recipient immovably: so that it does not remain in heretics and schismatics; and consequently they neither absolve nor excommunicate, nor grant indulgence, nor do anything of the kind, and if they do, it is invalid.De Romano Pontifice, Saint Robert Bellarmine: Saint Nicholas I (epist. Ad Michael) repeats and confirms the same. Finally, Saint Thomas also teaches (II-II, Q39, A3) that schismatics immediately lose all jurisdiction, and that anything they try to do on the basis of any jurisdiction will be null..He who deserts the Church will vainly believe that he is in the Church; Saint Cyprian (quoted in Amantissimus by Pope Pius IX, paragraph 3):Between heresy and schism, explains St. Jerome, there is this difference, that heresy perverts dogma, while schism, by rebellion against the bishop, separates from the Church. Nevertheless there is no schism which does not trump up a heresy to justify its departure from the Church. 
Michael Fighting
That they all may be one, as thou, Father, in me, and I in thee; that they also may be one in us: that the world may believe that thou hast sent me. John 17:21
Saint Cyprian (De Unitate Ecclesiae): He that keeps not the unity of the Church, does he think that to keep the faith? He that abandons the See of Peter whereon the church is founded, can he flatter himself that he is still in the Church?
