# 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.