Form-automorphism

Definition
Let $$V$$ be a variety of algebras and $$A \in V$$. A form-automorphism of $$A$$ with respect to $$V$$ is an automorphism of $$A$$ that arises from an automorphing form for $$V$$, viz an expression in one variable and $$k$$ parameters that is an automorphism for any fixed choice of the parameters for any algebra in the variety.

Weaker properties

 * Conditional form-automorphism
 * Form-endomorphism
 * Variety-extensible automorphism
 * Variety-pushforwardable automorphism
 * Variety-quotient-pullbackable automorphism