associator of a monoidal category

Let \(\mathcal{C}\) be a category with a monoidal structure. Then the associator is a natural isomorphism

\begin{align*} \alpha: (- \otimes -( \otimes - )) \rightarrow ((- \otimes -) \otimes -) \end{align*}

where

\begin{align*} \alpha_{x,y,z} \coloneqq \alpha (x,y,z): (x \otimes (y \otimes z)) \rightarrow ((x \otimes y) \otimes z) \end{align*}