##  [Bar Construction](/bar-construction) 

  ##  [Bar Construction](https://algebra.quantumdictionary.io/bar-construction-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

A standard simplicial or chain-level construction that produces a resolution of an augmented associative algebra or module, encoding extensions and enabling computation of derived functors such as Tor and Hochschild homology.