Definition:Direct Limit

Definition
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 $D$.

Also known as
A direct limit is also known as an inductive limit or directed colimit.

Also see

 * Definition:Inverse Limit