Primitive element of an atomic finite-surjection sheaf
= Primitive element of an atomic finite-surjection sheaf
An element $x\in F(n)$ is primitive if it does not descend along any surjection $n\to n-1$. All elements at cardinality one are primitive. Repeated descent reaches a primitive ancestor in finitely many steps, and the <primitive-element kernel rigidity lemma> makes the ancestor unique up to bijection.