Can. 751 Heresy is the obstinate denial or obstinate doubt after the reception of baptism of some truth which is to be believed by divine and Catholic faith….

The denial or doubt of heresy must be ‘obstinate’ because a mere passing doubt about an article of faith is not a heresy. Neither is a simple misunderstanding on what the Church teaches a heresy. Ignorance of Church teaching might be culpable, if the person is an adult who has neglected to learn his Faith in accord with his abilities, opportunities, and state of life. But mere ignorance is not heresy.

To be brief, let’s summarize ‘obstinate denial or obstinate doubt’ with the term rejection. A heresy is a rejection of some truth. Which truths? any truth to be believed by divine and Catholic faith.

The expression ‘divine and Catholic faith’ is from Vatican I:

8. Wherefore, by divine and Catholic faith all those things are to be believed which are contained in the word of God as found in Scripture and tradition, and which are proposed by the Church as matters to be believed as divinely revealed, whether by her solemn judgment or in her ordinary and universal magisterium.

The expression refers to the full assent of faith, i.e. to the exercise of the theological virtue of faith. The full assent of faith must be given to all truths which are both contained in Tradition or Scripture, and taught by the Magisterium under Papal infallibility, or in a solemn definition of an Ecumenical Council, or by the Universal Magisterium. Any such teaching is infallible, and the rejection of any such teaching is a heresy.

An infallible teaching of the Magisterium is a dogma, and so a heresy is essentially the rejection of a dogma.

Notice that, to be a heresy, an idea need not have been identified and called a heresy by the Magisterium. Rather, any idea which constitutes a substantial rejection of any teaching requiring the full assent of faith is an heretical idea. There is no teaching of the Magisterium asserting that nothing is a heresy unless the Magisterium has called it a heresy.

However, a problem arises with the above definition. In the history of the Church, there have been many heresies. The Fathers, Doctors, and Saints of the Church, as well as innumerable ordinary Catholic Christians, have always argued against heretical ideas, and called those ideas heresy, prior to any exercise of the infallible Magisterium.

So we should include in the definition of heresy any rejection of any infallible teaching of Tradition or Scripture. For the term dogma pertains to what must be believed, but the faithful must believe the teachings of Tradition and Scripture, not only the teachings of the Magisterium. For example, in the early Church, there were very few, if any, infallible teachings of the Magisterium. Were the faithful then free to believe anything they wished? Not at all. For St. Paul, writing under the inspiration of the Holy Spirit, says:

[Titus]
{3:10} Avoid a man who is a heretic, after the first and second correction,
{3:11} knowing that one who is like this has been subverted, and that he offends; for he has been condemned by his own judgment.

[1 Corinthians]
{11:18} First of all, indeed, I hear that when you assemble together in the church, there are schisms among you. And I believe this, in part.
{11:19} For there must also be heresies, so that those who have been tested may be made manifest among you.

There were heresies in the very early Church, and the terms heresy and heretic were used, despite the lack of any infallible magisterial teaching contradicting the heresy.

Also, when Jesus argued against the heresies of the scribes and Pharisees, He did not argue on the basis that He was exercising the Magisterium, nor did He condemn false teachings without any explanation. Rather, He argued against and condemned these false teachings based on Tradition and Scripture. So a rejection of any infallible teaching of Tradition or Scripture or Magisterium is a heresy, just as any infallible teaching of Tradition or Scripture or Magisterium is a dogma.

Now an infallible teaching of Tradition or Scripture, which has not yet been infallibly taught by the Magisterium, is distinguished from infallible teachings of Tradition or Scripture that have also been taught infallibly by the Magisterium. The former is called material dogma, and the latter is called formal dogma. However, the terms material heresy and formal heresy do not align with material and formal dogma. Rather, the terms ‘material’ and ‘formal’ have different meanings when applied respectively to dogma and to heresy. Material heresy is the heretical idea itself, whereas formal heresy is the knowing and willful assertion of material heresy. Material heresy is not an act of a person; it is an idea. Formal heresy is the act whereby a person knowingly chooses the sin of adhering to material heresy.