Isomorphism Preserves Semigroups/Proof 2

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Theorem

Let $\struct {S, \circ}$ and $\struct {T, *}$ be algebraic structures.

Let $\phi: S \to T$ be an isomorphism.


If $\struct {S, \circ}$ is a semigroup, then so is $\struct {T, *}$.


Proof

An isomorphism is an epimorphism.

The result follows as a direct corollary of Epimorphism Preserves Semigroups.

$\blacksquare$