I’m copying here another formulation:
There is a dispute at the beginning of tractate Bava Kamma between Rabbi Eliezer and the Sages as to whether someone who performed both a primary category of labor and a derivative on the Sabbath is liable for two sin offerings or only one. Some wanted to make this depend on the conceptual question whether a derivative prohibition on the Sabbath actually constitutes a prohibition in its own right, in which case he would be liable for 2 sin offerings because these are two prohibitions, or whether it is part of the labor prohibition of the primary category, in which case he would be liable for only one sin offering because it is one prohibition-name.
I wondered whether this might depend on the question what exactly a person brings a sin offering for: for the act of transgression itself (in our case, desecration of the Sabbath), or for the negligence that led him to it. Assuming that the sin offering comes for the negligence, one could say that even if a primary category and its derivative are two different prohibitions, he would still be liable for only one sin offering, because there is a similarity between the primary category and the derivative (in purpose or mode of action), and therefore the person really had to be careful about one thing (not to do anything whose purpose/mode of action is x), and so he brings only one sin offering. What do you think?

I don’t understand why, if the sin offering is brought for negligence, one could bring a single sin offering for a primary category and its derivative, even if these are two different prohibitions. How is this different from two completely different prohibitions, where it is obvious that two sin offerings are brought? The fact that there is a certain similarity between a primary category and its derivative is true, but I don’t see why that leads to liability for only one sin offering.
By the way, in my article on causing a secular Jew to stumble, I wrote that in my opinion a sin offering is brought for negligence, and therefore the distinctions between sin offerings follow the number of negligent lapses of awareness, not the number of transgressions.

What I meant was that even though these are two prohibitions, one can say that this is only one lapse of awareness, because the person was supposed to remember one fact—namely, that he must avoid actions whose purpose/mode of operation is x (which is what the primary category and the derivative have in common), and at the end of the day that is one thing. I am arguing that regarding lapse of awareness, we are less interested in how the things are defined from a halakhic standpoint and more interested in their implications for the person; and therefore, if from the person’s perspective the implications can be reduced to one category, then he should bring only one sin offering.

I completely disagree. The lapses of awareness relate to the prohibitions in their halakhic definitions. The similarity between a primary category and its derivative is irrelevant. There may also be similarity between different prohibitions. Just as an illustration, think about the primary categories and derivatives of building as I defined them in the column that dealt with this. There is no practical similarity at all between making cheese and pitching a tent, even though both are derivatives of building.

And likewise with winnowing, selecting, and sifting, which are three different primary categories that are completely similar to one another