  Let $G$ be a group and let $X$ be an algebraic variety over an algebraically
closed field $k$ of characteristic zero. Denote $A=X(k)$ the set of rational
points of $X$. We investigate invertible algebraic cellular automata $\tau
\colon A^G \to A^G$ whose local defining map is induced by some morphism of
algebraic varieties $X^M \to X$ where $M$ is a finite memory. When $G$ is
locally embeddable into finite groups (LEF), then we show that the inverses of
reversible algebraic cellular automata are automatically algebraic cellular
automata. Generalizations are also obtained for finite product Hopfian pointed
object alphabets in concrete categories.
