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Yeah, it's a reference to how "category theory" generalizes "group theory". So if transformations in a group are called "symmetries" then you might call the tra
by mathgenius 3y ago
Yeah, it's a reference to how "category theory" generalizes "group theory". So if transformations in a group are called "symmetries" then you might call the transformations in a category "generalized symmetries" or "non-invertible symmetries" as in this article.
- throwaway81523 3y agoErm the whole idea of a symmetry is that it is a group invariant. If they're using the term in some more general way, it would help if they said what the new way was. The article is otherwise almost completely uninformative. What on earth is a "generalized symmetry", especially one that still has something like a conservation law? Does it have applications in math as well as physics? E.g. topologists are always looking for new invariants. I can understand that popularizations have to gloss over the math, but they usually at least identify the important points even if they don't get into the weeds of explaining the details. This seems like more of a sleight of hand.
- Robotbeat 3y agoRead the original paper: https://arxiv.org/abs/1412.5148 https://arxiv.org/abs/1412.5148