Definition:Direct Limit of Sequence of Groups/Definition 2

Definition

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 $G_\infty$.

Also see

• Equivalence of Definitions of Direct Limit of Sequence of Groups
• Existence and Uniqueness of Direct Limit of Sequence of Groups

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 5.6$: Example $5.29$