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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 at 0:42
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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 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 at 3:01
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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 at 4:49
    
@Mariano: I thought it was named after the examples coming from loop group representat –  Qiaochu Yuan Apr 26 at 5:02
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@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 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 at 17:16

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