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I want to translate the terminology “fusion category” into Chinese, so I should know the exact meaning of "fusion". There are two translations in Oxford Advanced Learner’s Dictionary:

1.the process or result of joining two or more things together to form one

2.(also nuclear fusion )( physics )the act or process of combining the nuclei(= central parts) of atoms to form a heavier nucleus, with energy being released

Which one? Or something else?

Maybe, the first one is a better choice. Who can tell me? Thank you in advance.

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the first, this is definitely not physics. – Carlo Beenakker Apr 26 '14 at 0:42
I'll add that the second one is just a special case of the first one (where the things being joined are the nuclei of the atoms) – Denis Nardin Apr 26 '14 at 1:43

1 Answer 1

up vote 7 down vote accepted

I think that

$$ \text{"the process or result of joining two or more things together to form one"} $$

Is a good description, that also reflects the origin of the terminology in the term "fusion category". Here, the things that are being joined (=fused) are the objects of the category, and the new entity that they form after fusion is their product (also called tensor product, or fusion product) in the category.

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"Fusion" was used in group theory before fusion categories came about, in contexts as that of Burnside's fusion theorem and fusion systems, which show up in CFG theory. I always thought that fusion categories are so called because they ressemble/remind us of fusion systems. – Mariano Suárez-Alvarez Apr 26 '14 at 3:01
Thank all of you! I will use "融合范畴" as the translation of "fusion category". It adopts the first meaning. – Jingcheng Dong Apr 26 '14 at 4:49
@Mariano: That doesn't make any sense to me. As far as I can tell, the term fusion comes from conformal field theory; I really don't think they were thinking about representations in characteristic p. – Ben Webster Apr 26 '14 at 6:51
@Mariano: I've always thought the name comes from representation theory and quantum mechanics. Physicists sometimes call tensor product "fusion product", and talk about "fusion rules" for irreps. – Peter Dalakov Apr 26 '14 at 17:16
I agree with Ben. Namely, I'm completely certain that the term "fusion" in "fusion category" and in "fusion system" are unrelated. The first one comes from conformal field theory: in CFT one talks of field insertions at certain points on a Riemann surface (translate: field = object of a category) and one is interested at what happens when two points are made to collide. The mathematics that governs those kinds of things is actually that of braided fusion categories (more specifically, modular tensor categories), but the notion of fusion category --without a braiding-- is closely related. – André Henriques Apr 27 '14 at 4:48

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