Monoidal Category

A monoidal category is a 2-category C with:

• a ‘tensor product’ $\otimes :C$
• a unit $1$.
• an associator $\alpha :X\otimes (Y\otimes Z)\cong (X\otimes Y)\otimes Z$,
• left unitor $\lambda :$ $1\otimes X\cong X$
• right unitor $\rho :$ X$\otimes$ $1\cong X$
• that satisfies a triange and pentagon coherence laws