Title: Tables of practical invariants for distinguishing multiplicity-free fusion categories up to rank 7 Show Chinese title

Title: 至7阶的无重数融合范畴的实用不变量表

Abstract: This paper discusses to what extent the census of multiplicity-free fusion categories up to rank 7, proposed by the software package Anyonica and the anyonwiki website, can be regarded as a proper classification. The questions of correctness and completeness are briefly discussed, and the question of inequivalence of the provided categories is resolved under the assumption that all proposed data is correct. This is done by providing tables of small sets of invariants for these categories, for which (a) their invariance under automorphisms can be checked manually, and (b) the (in)equivalence of two skeletal fusion categories can be checked manually. These invariants can also be used to identify the category on the anyonwiki that corresponds to one for which the skeletal data is known. Show Chinese abstract

Abstract: 本文讨论了由软件包Anyonica和anyonwiki网站提出的至秩7的无重数融合范畴的普查在多大程度上可以被视为适当的分类。 正确性和完备性的问题进行了简要讨论，并在假设所有提出的数据正确的前提下解决了所提供范畴的非等价性问题。 这是通过为这些范畴提供小集合的不变量表来完成的，这些不变量满足：(a) 可以手动检查其在自同构下的不变性，以及(b) 可以手动检查两个骨架构造的融合范畴的(非)等价性。 这些不变量还可以用于识别anyonwiki上与已知骨架构造对应的范畴。