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68 |
68 |
69 For 1-categories based on Spin balls, |
69 For 1-categories based on Spin balls, |
70 the nontrivial spin homeomorphism from $B^1$ to itself which covers the identity |
70 the nontrivial spin homeomorphism from $B^1$ to itself which covers the identity |
71 gives an order 2 automorphism of $c(\cX)^1$. |
71 gives an order 2 automorphism of $c(\cX)^1$. |
72 There is a similar involution on the objects $c(\cX)^0$. |
72 There is a similar involution on the objects $c(\cX)^0$. |
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73 In the case where there is only one object and we are enriching over complex vector spaces, this |
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74 is just a super algebra. |
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75 The even elements are the $+1$ eigenspace of the involution on $c(\cX)^1$, |
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76 and the odd elements are the $-1$ eigenspace of the involution. |
73 |
77 |
74 For 1-categories based on $\text{Pin}_-$ balls, |
78 For 1-categories based on $\text{Pin}_-$ balls, |
75 we have an order 4 antiautomorphism of $c(\cX)^1$. |
79 we have an order 4 antiautomorphism of $c(\cX)^1$. |
76 For 1-categories based on $\text{Pin}_+$ balls, |
80 For 1-categories based on $\text{Pin}_+$ balls, |
77 we have an order 2 antiautomorphism and also an order 2 automorphism of $c(\cX)^1$, |
81 we have an order 2 antiautomorphism and also an order 2 automorphism of $c(\cX)^1$, |