Isomorphism

Isomorphism is a relation between mathematical objects that expresses the commonality of their structure; it is used in different branches of mathematics and is defined in each of them depending on the structural properties of the objects under study. Usually, isomorphism is defined for sets endowed with some structure, for example, groups, rings, or vector spaces; in that case, it is defined as an invertible mapping (bijection) between two structured sets that preserves the structure, thus showing that the objects are “organized in the same way” with respect to that structure. If an isomorphism exists between objects, they are called isomorphic. Isomorphism always defines an equivalence relation on the class of such structures.