##  [Failure of Exactness](/failure-exactness) 

  ##  [Failure of Exactness](https://algebra.quantumdictionary.io/failure-exactness-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A situation where a sequence of homomorphisms ...→A_{i-1}→A_i→A_{i+1}→... fails to be exact at some position i, meaning the image of the incoming map is not equal to the kernel of the outgoing map; homology groups measure this failure.