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Nicolas Cage
Nicolas Cage
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In arxiv:0909.3140 the $G$-extensions of a fusion category $\mathcal{D}$ are classified via monoidal 2-functors $G \to \underline{\underline{BrPic}}(\mathcal{D})$. A crucial part of the classification is Theorem 7.7 that shows that equivalence classes of such functors are in 1-1 correspondence with equivalence classes of $G$-extensions of $\mathcal{D}$. However in the proof they never show that the tensor categories they obtain from such functors are actually rigid. I was also unable to find this statement anywhere else in the paper, it is not even mentioned. Is there some obvious proof of this that I am missing or are they in fact classifying not necessarily rigid $G$-extensions? (The latter would however contradict Definition 2.1, which defines a G-extension to be in particular a fusion category, hence rigid.)

In arxiv:0909.3140 the $G$-extensions of a fusion category $\mathcal{D}$ are classified via monoidal 2-functors $G \to \underline{\underline{BrPic}}(\mathcal{D})$. A crucial part of the classification is Theorem 7.7 that shows that equivalence classes of such functors are in 1-1 correspondence with equivalence classes of $G$-extensions of $\mathcal{D}$. However in the proof they never show that the tensor categories they obtain from such functors are actually rigid. I was also unable to find this statement anywhere else in the paper, it is not even mentioned. Is there some obvious proof of this that I am missing or are they in fact classifying not necessarily rigid $G$-extensions?

In arxiv:0909.3140 the $G$-extensions of a fusion category $\mathcal{D}$ are classified via monoidal 2-functors $G \to \underline{\underline{BrPic}}(\mathcal{D})$. A crucial part of the classification is Theorem 7.7 that shows that equivalence classes of such functors are in 1-1 correspondence with equivalence classes of $G$-extensions of $\mathcal{D}$. However in the proof they never show that the tensor categories they obtain from such functors are actually rigid. I was also unable to find this statement anywhere else in the paper, it is not even mentioned. Is there some obvious proof of this that I am missing or are they in fact classifying not necessarily rigid $G$-extensions? (The latter would however contradict Definition 2.1, which defines a G-extension to be in particular a fusion category, hence rigid.)

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Nicolas Cage
Nicolas Cage
  • 203
  • 1
  • 6

In arxiv:0909.3140arxiv:0909.3140 the $G$-extensions of a fusion category $\mathcal{D}$ are classified via monoidal 2-functors $G \to \underline{\underline{BrPic}}(\mathcal{D})$. A crucial part of the classification is Theorem 7.7 that shows that equivalence classes of such functors are in 1-1 correspondence with equivalence classes of $G$-extensions of $\mathcal{D}$. However in the proof they never show that the tensor categories they obtain from such functors are actually rigid. I was also unable to find this statement anywhere else in the paper, it is not even mentioned. Is there some obvious proof of this that I am missing or are they in fact classifying not necessarily rigid $G$-extensions?

In arxiv:0909.3140 the $G$-extensions of a fusion category $\mathcal{D}$ are classified via monoidal 2-functors $G \to \underline{\underline{BrPic}}(\mathcal{D})$. A crucial part of the classification is Theorem 7.7 that shows that equivalence classes of such functors are in 1-1 correspondence with equivalence classes of $G$-extensions of $\mathcal{D}$. However in the proof they never show that the tensor categories they obtain from such functors are actually rigid. I was also unable to find this statement anywhere else in the paper, it is not even mentioned. Is there some obvious proof of this that I am missing or are they in fact classifying not necessarily rigid $G$-extensions?

In arxiv:0909.3140 the $G$-extensions of a fusion category $\mathcal{D}$ are classified via monoidal 2-functors $G \to \underline{\underline{BrPic}}(\mathcal{D})$. A crucial part of the classification is Theorem 7.7 that shows that equivalence classes of such functors are in 1-1 correspondence with equivalence classes of $G$-extensions of $\mathcal{D}$. However in the proof they never show that the tensor categories they obtain from such functors are actually rigid. I was also unable to find this statement anywhere else in the paper, it is not even mentioned. Is there some obvious proof of this that I am missing or are they in fact classifying not necessarily rigid $G$-extensions?

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Nicolas Cage
Nicolas Cage
  • 203
  • 1
  • 6

Why are $G$-Extensions of fusion categories rigid, when constructed via monoidal 2-functors $G \to \underline{\underline{BrPic}}(\mathcal{D})$?

In arxiv:0909.3140 the $G$-extensions of a fusion category $\mathcal{D}$ are classified via monoidal 2-functors $G \to \underline{\underline{BrPic}}(\mathcal{D})$. A crucial part of the classification is Theorem 7.7 that shows that equivalence classes of such functors are in 1-1 correspondence with equivalence classes of $G$-extensions of $\mathcal{D}$. However in the proof they never show that the tensor categories they obtain from such functors are actually rigid. I was also unable to find this statement anywhere else in the paper, it is not even mentioned. Is there some obvious proof of this that I am missing or are they in fact classifying not necessarily rigid $G$-extensions?