There has been some confusion in the discussion here about whether the work https://arxiv.org/abs/2210.06279 https://arxiv.org/abs/2210.06279 is actually about

There has been some confusion in the discussion here about whether the work https://arxiv.org/abs/2210.06279 https://arxiv.org/abs/2210.06279 is actually about category theory. To clarify the confusion, here is a snippet from the abstract. > The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average number of epimorphisms to a fixed object. So the work is about category theory. The confusion comes in because the Quanta article focuses on what is expected to be the most important application of the work, which is in the study of ideal class groups from number theory. That is, the authors will try to (but have not yet) use their theory on the category of groups in order to make progress on the Cohen-Lenstra heuristics. I'm not qualified to judge the significance of their work here since all of the math goes over my head. Taking the authors' words, > This is a significant advance, as previous work has always relied on a priori knowing a distribution with certain moments. Being able to construct a distribution from its moments opens new avenues such as in our subsequent paper mentioned above I guess we will find out if/when their subsequent paper on the Cohen-Lenstra heuristics comes out.