We are going to deal with groups, but it probably works with other algebraic structures.
Think of a collection of groups $\{A_n\}_{n=0}^{\infty}$ and morphisms:
$$ \theta_{n+1}:A_{n+1} \rightarrow A_n $$We call this an inverse system. And we call a coherent sequence to a sequence $(a_i)$ such that
$$ \theta_{i+1}(a_{i+1})=a_i $$The group of all these sequences is called the inverse limit and is usually denoted by
$$ \lim _{\leftarrow} A_{n} $$[Atiyah 2018] page 103
________________________________________
________________________________________
________________________________________
Author of the notes: Antonio J. Pan-Collantes
INDEX: