Example 2.1.5.22. Let $\operatorname{Set}$ denote the category of sets, equipped with the cartesian monoidal structure of Example 2.1.3.2. Then we can identify algebra objects of $\operatorname{Set}$ with monoids. More precisely, there is a canonical isomorphism of categories $\operatorname{Alg}(\operatorname{Set}) \simeq \operatorname{Mon}$, where $\operatorname{Mon}$ denotes the category of monoids (Definition 1.3.2.3).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$