The data of a symmetric monoidal category $(\mathsf{V},\otimes,{})$ consists of a category $\mathsf{V}$, a bifunctor $-\otimes -\colon \mathsf{V} \times \mathsf{V} \to \mathsf{V}$ called the monoidal product, and a unit object ${} \in \mathsf{V}$ together with specified natural isomorphisms \(v\otimes w \underset{\gamma}{\cong} w \otimes v \qquad u \otimes (v \otimes w) \underset{\alpha}{\cong} (u \otimes v) \otimes w \qquad {*} \otimes v \underset{\lambda}{\cong} v \underset{\rho}{\cong} v \otimes *\) witnessing symmetry, associativity, and unit conditions on the monoidal product. The natural transformations \eqref{eq:symmonisos} must satisfy certain ``coherence conditions’’ that will be discussed momentarily. A mon-oid-al category is defined similarly, except that the first symmetry natural isomorphism is omitted.