# Function property

The function property must satisfy isomorphism-invariance: if $f_1:G \to G$ and $f_2:H \to H$ are functions, and there is an isomorphism $\sigma:G \to H$ such that $\sigma \circ f_1 = f_2 \circ \sigma$, then $f_1$ satisfies the function property iff $f_2$ satisfies the function property.