A parity concept for invertible morphisms yields a coherence theorem in symmetric monoidal categories, with the free permutative category on an invertible generator equivalent to the super integers via ±1.
Dugger, Coherence for invertible objects and multigraded homotopy rings, Algebr
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Invertibility and parity in symmetric monoidal categories
A parity concept for invertible morphisms yields a coherence theorem in symmetric monoidal categories, with the free permutative category on an invertible generator equivalent to the super integers via ±1.