##  [Koszul Duality](/koszul-duality) 

  ##  [Koszul Duality](https://algebra.quantumdictionary.io/koszul-duality-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 relationship between certain quadratic (or quadratic-like) algebraic objects and their homological duals, typically realized via bar and cobar constructions or by taking Ext-algebras; it identifies an algebra with a derived or homotopical dual object whose homology encodes the original algebra’s resolutions.