monoidal structure

Let \(\mathcal{C}\) be a category. aA monoidal structure on \(\mathcal{C}\) consists of

1. a tensor functor

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

1. a tensor unit \(1 \in \mathcal{C}\)
2. natural isomorphisms a) associator of a monoidal category b) left unitor of a monoidal category c) right unitor in a monoidal category

such that following diagrams commutes

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