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Answer by Morgan Rogers for Free enriched monoidal categories
A silly counterexample can be obtained by considering $\mathcal{V} = \mathrm{FinSet}_{\mathrm{bij}}$, the category of finite sets and bijections, with product of sets as the monoidal operation....
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Suppose $(\mathcal{V},\otimes,1)$ is a symmetric monoidal category and $\mathbb{C}$ is a $\mathcal{V}$-category. I will deliberately avoid usual powerful assumptions (eg completeness/cocompleteness) on...
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