tensor functor of a monoidal category

Let \(\mathcal{C}\) be a monoidal category category. then the tensor functor is a designated functor

\begin{align*} \otimes: \mathcal{C} \times \mathcal{C} \rightarrow \mathcal{C} \end{align*}

satisfying

1. triangle identity of a monoidal category
2. pentagon identity