##  [Failure of Projectivity](/failure-projectivity) 

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

  

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**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The property that an object is not projective: it does not satisfy the universal lifting/splitting property and therefore fails to split some extensions or to admit certain homotopy‑lifting maps.