Example 2.1.6.6. Let $M$ and $M'$ be monoids, regarded as monoidal categories having only identity morphisms (Example 2.1.2.8). Then lax monoidal functors from $M$ to $M'$ (in the sense of Definition 2.1.5.8) can be identified with monoid homomorphisms from $M$ to $M'$ (in the sense of Definition 1.3.2.3). Moreover, every lax monoidal functor from $M$ to $M'$ is automatically strict monoidal (and therefore monoidal).
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