Homomorphism

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Let $A$ and $B$ be algebraic structures of the same species, for example two groups or fields. A homomorphism is a function $\phi : A \to B$ that preserves the structure of the species.

For example, if $A$ is a substructure (subgroup, subfield, etc.) of $B$ , the inclusion map $i: A \to B$ such that $i(a) = a$ for all $a \in A$ is a homomorphism.

A homomorphism from a structure to itself is called an endomorphism. A homomorphism that is bijective is called an isomorphism. A bijective endomorphism is called an automorphism.