nLab multiplicity free fusion category


A multiplicity free fusion category is a fusion category in which all of the fusion coefficients are 00 or 11.

That is, a fusion category 𝒞\mathcal{C} is multiplicity free if for all simple objects A,BA,B we have that ABA\otimes B is a direct sum of simple objects, each isomorphism class appearing with multiplicity at most 11.

Equivalently, this means that the spaces Hom(AB,C)\text{Hom}(A\otimes B,C) and Hom(C,AB)\text{Hom}(C,A\otimes B) are at most one dimensional for all triples of simple objects A,B,CA,B,C.

Created on July 19, 2023 at 16:24:04. See the history of this page for a list of all contributions to it.