[karmakaze]

> In work published in the Annals of Mathematics in 2016, Ellenberg, along with Akshay Venkatesh and Craig Westerland, used moments to study the statistics of class groups in a slightly different setting than Cohen and Lenstra had considered. This idea was reused several times. But each time researchers used the moments, they would lean on the quirks of their particular problem to prove that the infinite set of equations had a solution. That meant their techniques were not transferable. The next mathematician who needed to use moments would have to solve the moment problem all over again.

Are you suggesting that this need to solve the moment problem all over again could have been avoided by searching Category Theory developments?