##  [Mapping Cone Construction](/mapping-cone-construction) 

  ##  [Mapping Cone Construction](https://algebra.quantumdictionary.io/mapping-cone-construction-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 construction that associates to a chain map between complexes a new complex (the mapping cone) whose homology measures the failure of the map to be a quasi-isomorphism and that yields long exact sequences in homology.