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André Henriques
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The symmetric monoidal category $\mathit{sVect}$ of super vector spaces has a non-trivial autoequivalence $J$.

The symmetric monoidal functor $J:\mathit{sVect}\to \mathit{sVect}$ is the identity at the level of objects and at the level of morphisms. But the coherence $J(V \otimes W) \xrightarrow{\cong} J(V) \otimes J(W)$ is non-trivial. It is given by $-1$ on $V_{odd} \otimes W_{odd}$ and $+1$ on the rest.

The image of $\mathit{Cliff}(V,q)$ under $J$ is $\mathit{Cliff}(V,-q)$. So anything that you do with one convention can equally well be done with the other convention.


Now, as far as practical things are concerned, I would recommend minimizing the number of minus signs that you end up writing down.
André Henriques
  • 43.2k
  • 5
  • 130
  • 264