 Irreducible representable sheaf for the regular coverage

If a family of subsheaves covers $yA$, local membership of $1_A$ gives a regular epimorphism $\alpha :B\to A$ belonging to one subsheaf. The sheaf condition descends that section to $1_A$ in the same subsheaf. All maps into $A$ are restrictions of $1_A$, so that subsheaf is $yA$. Thus representable sheaves for the regular coverage are irreducible even for arbitrary unions.