##  [Isomorphism](/isomorphism) 

  ##  [Isomorphism](https://natural.quantumdictionary.io/isomorphism-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A bijective structure-preserving map between two mathematical objects whose inverse is also structure-preserving; it identifies the objects as the same up to the specified structure.

 

 

 

 

 





 

 



 ##  [Isomorphism](https://mathlogic.quantumdictionary.io/isomorphism-1) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A bijective mapping between two mathematical objects that preserves the relevant structure (operations, relations, or distinguished elements) and whose inverse likewise preserves that structure; it identifies the objects as the same up to the structure in question.

 

 

 

 

 





 

 



 ##  [Isomorphism](https://puremath.quantumdictionary.io/isomorphism-2) 

  

 [![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

An isomorphism is a bijective homomorphism between two algebraic structures whose inverse map is also a homomorphism; it exhibits the two structures as structurally identical within the chosen signature.

 

 

 

 

 





 

 



 ##  [Isomorphism](https://algebra.quantumdictionary.io/isomorphism-3) 

  

 [![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 homomorphism that is bijective and whose inverse is also a homomorphism; it establishes an equivalence of algebraic structures so that the two objects have the same algebraic form.