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Example Let $\operatorname{Set}$ denote the category of sets, endowed with the monoidal structure given by cartesian product of sets (Example For each set $S$, we can identify nonunital algebra structures on $S$ (in the sense of Example with nonunital monoid structures on $S$ (in the sense of Definition This observation supplies an isomorphism of categories $\operatorname{Alg}^{\operatorname{nu}}( \operatorname{Set}) \simeq \operatorname{Mon}^{\operatorname{nu}}$, where $\operatorname{Mon}^{\operatorname{nu}}$ is the category of Definition