Definition:Inverse Limit of Inverse System of Groups

Definition

Let $\sequence {G_n}_{n \mathop \in \N}$ be a inverse system of groups with group homomorphisms $\sequence {\theta_n}_{n \mathop \in \N_{>0} }$.

The inverse limit of $\sequence {G_n}$ is the group consisting of all coherent sequences of $\sequence {G_n}$.

It is written as:

$\varprojlim G_n$

Sources

• 1969: M.F. Atiyah and I.G. MacDonald: Introduction to Commutative Algebra: Chapter $10$: Completion