Definition 4.43.9. A quadruple (\mathcal{C}, \otimes , \phi , \psi ) where \mathcal{C} is a category, \otimes : \mathcal{C} \otimes \mathcal{C} \to \mathcal{C} is a functor, \phi is an associativity constraint, and \psi is a commutativity constraint compatible with \phi is called a symmetric monoidal category if there exists a unit.
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