##  [Homotopy Extension Property](/homotopy-extension-property) 

  ##  [Homotopy Extension Property](https://puremath.quantumdictionary.io/homotopy-extension-property-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A property of an inclusion i:A→X (or of the pair (X,A)) that any homotopy H_t defined on A can be extended to a homotopy ˜H_t on X starting from any map f:X→Y restricting to the given homotopy on A; equivalently a recognition criterion for cofibrations in many settings.