Definition:Direct Limit

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Let $\mathbf C$ be a category.

Let $I$ be a directed ordered 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