\begin{definition}[Definition:Direct Limit]
Let $\mathbf C$ be a category.
Let $I$ be an upward directed set.
Let $\mathbf I$ be the order category of $I$.
Let $D : \mathbf I \to \mathbf C$ be a diagram.
The '''direct limit''' of $D$ is the colimit of the diagram $D$.
\end{definition}