##  [Clone of Operations](/clone-operations) 

  ##  [Clone of Operations](https://puremath.quantumdictionary.io/clone-operations-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

On a set A, a clone is a collection C of finitary operations on A that contains all projection maps and is closed under composition (substitution): composing operations from C (of appropriate arities) yields an operation in C. Abstractly, clones encode all term operations definable from a given signature on the same carrier.