\begin{definition}[Definition:Direct Limit of Sequence of Groups/Definition 2]
Let $\N$ be the order category on the natural numbers.
Let $\mathbf{Grp}$ be the category of groups.
Let $G: \N \to \mathbf{Grp}$ be an $\N$-diagram in $\mathbf{Grp}$.
A '''direct limit''' for $G$ is a colimit ${\varinjlim \,}_n \, G_n$, and is denoted $G_\infty$.
\end{definition}