According to both nlab and wikipedia, PROPS are defined as special kinds of strict symmetric monoidal categories and morphisms between them are defined as strict symmetric monoidal functors. Why is strictness required? I can understand requiring the categories to be strict since every symmetric monoidal category is equivalent to a strict one. So strictness can make working with them easier. But requiring the functors to be strict seems unnatural. Is there a conceptual reason for requiring the functors to be strict?
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