The isomorphism of categories of Example 9.2.3.1.1 restricts to an isomorphism
where $\mathsf{Grpd}$ is the full subcategory of $\mathsf{Cats}$ spanned by the groupoids.In other words, we have an identification
\[ \webleft\{ \text{Groups}\webright\} \cong \webleft\{ \text{One-object groupoids}\webright\} . \]