Homomorphism

https://en.wikipedia.org/wiki/Homomorphism

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).

In every category of algebraic structures, an isomorphism is a homomorphism that is a bijection.

https://en.wikipedia.org/wiki/Homomorphism

Homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, two vector spaces).

The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory.

A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. Each of those can be defined in a way that may be generalized to any class of morphisms.