A Monoidal category is a category with an associated biendofunctor that has an identity, which satisfies Mac Lane''s pentagonal and triangular coherence conditions Technically we usually say that category is Monoidal, but since most interesting categories in our world have multiple candidate bifunctors that you can use to enrich their structure, we choose here to think of the bifunctor as being monoidal. This lets us reuse the same Bifunctor over different categories without painful newtype wrapping.