Delooping of a Group

Let $G$ be a Group. Its delooping $\mathbf{B}G$ is a single-object Groupoid, that has an Isomorphism for every $g:G$.

Alternatively, the delooping of a group is the Delooping of its underlying monoid: this yields an identical category, but is a slightly different perspective that considers groups as monoids with a property, as opposed to their own algebraic structure.