Isomorphism Preserves Associativity/Proof 2

Theorem

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

Let $\phi: \struct {S, \circ} \to \struct {T, *}$ be an isomorphism.


Then $\circ$ is associative if and only if $*$ is associative.


Proof

An isomorphism is a fortiori an epimorphism.

The result follows from Epimorphism Preserves Associativity.

$\blacksquare$

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