Category:Definitions/Semigroup Homomorphisms

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This category contains definitions related to Semigroup Homomorphisms.
Related results can be found in Category:Semigroup Homomorphisms.

Let $\left({S, \circ}\right)$ and $\left({T, *}\right)$ be semigroups.

Let $\phi: S \to T$ be a mapping such that $\circ$ has the morphism property under $\phi$.

That is, $\forall a, b \in S$:

$\phi \left({a \circ b}\right) = \phi \left({a}\right) * \phi \left({b}\right)$

Then $\phi: \left({S, \circ}\right) \to \left({T, *}\right)$ is a semigroup homomorphism.