symmetric monoidal category

Let \(\mathcal{C}\) be a monoidal category with tensor functor \(\otimes\). Then \(\mathcal{C}\) is said to be a symmetric monoidal category, if there exists a natural isomorphism

\begin{align*} \eta: -_1 \otimes -_2 \rightarrow -_2 \otimes -_1 \end{align*}

i.e. natural isomorphisms

\begin{align*} A \otimes B \cong B \otimes A \end{align*}