##  [Dimension Shifting](/dimension-shifting) 

  ##  [Dimension Shifting](https://algebra.quantumdictionary.io/dimension-shifting-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 homological technique that replaces Ext or Tor groups in one degree by Ext or Tor groups in other degrees using short exact sequences together with projective or injective resolutions, producing canonical isomorphisms between different degrees under suitable vanishing hypotheses.