Remarks on Units of Skew Monoidal Categories

This article shows that the axioms of a skew monoidal category are independent and that its unit is unique up to a unique isomorphism together with an analogue of this result for monoidal functors between skew monoidal categories. It is also noted that these results carry over to skew monoidales before some benefits of certain extra structure on the unit maps of a skew monoidal category are discussed.