Category:Inverse of Algebraic Structure Isomorphism is Isomorphism

This category contains pages concerning Inverse of Algebraic Structure Isomorphism is Isomorphism:

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

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

Then $\phi$ is an isomorphism if and only if $\phi^{-1}: \struct {T, *} \to \struct {S, \circ}$ is also an isomorphism.