##  [Tor Obstruction](/tor-obstruction) 

  ##  [Tor Obstruction](https://algebra.quantumdictionary.io/tor-obstruction-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 nonzero element in a Tor group that indicates failure of the tensor product to preserve exactness or the failure of flatness; such an element obstructs naive tensoring operations or lifts that rely on exactness of ⊗.