##  [Direct Limit](/direct-limit) 

  ##  [Direct Limit](https://algebra.quantumdictionary.io/direct-limit-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The colimit of a directed (direct) system of objects and structure-preserving maps: an object together with canonical maps from each stage that is universal for receiving compatible maps from the system; elements are represented by equivalence classes of elements from some stage under eventual identification.