# Isomorphism definition

(biology) The similarity in form of organisms of different ancestry.

(chemistry) The similarity in the crystal structures of similar chemical compounds.

(sociology) The similarity in the structure or processes of different organizations.

2. A one-to-one correspondence.

(group algebra) A bijection f such that both f and its inverse f^{ −1} are homomorphisms, that is, structure-preserving mappings.

(computer science) A one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets.

(category theory) A morphism which has an inverse; the composition of the morphism and its inverse yields either one of two identity morphisms (depending on the order of composition).

## Other Word Forms

### Noun

## Origin of isomorphism

*iso-*+*-morphism*### From Wiktionary