Example 2.1.5.15. Let $k$ be a field, let $\operatorname{Vect}_{k}$ denote the category of vector spaces over $k$, and let $F: \operatorname{Vect}_{k} \rightarrow \operatorname{Set}$ be the forgetful functor, endowed with the nonunital lax monoidal structure described in Example 2.1.4.5. Then $F$ is a lax monoidal functor: the function
\[ \epsilon : \{ \ast \} \rightarrow F(k) \quad \quad \epsilon (\ast ) = 1 \in k \]
is a left and right unit for $F$.