2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72484A (v,0)-semilattice is ultraboolean, if it is a directed union of finite Boolean (v,0)-semilattices. We prove that every distributive (v,0)-semilattice is a retract of some ultraboolean (v,0)-semilattices. This is established by proving that every finite distributive (v,0)-semilattice is a retract of some finite Boolean (v,0)-semilattice, and this in a functorial way. This result is, in turn, obtained as a particular case of a category-theoretical result that gives sufficient conditions, for a functor $ Pi$, to admit a right inverse. The particular functor $ Pi$ used for the abovementioned result about ultraboolean semilattices has neither a right nor a left adjoint.General MathematicsCategory TheoryAMS: 18A30, 18A25, 18A20, 06A12, 06D05, 08B25, 18A40text