2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109144We prove Artin's axioms satisfy a compatibility for composition of 1-morphisms of stacks in groupoids. Consequently, some natural stacks in groupoids are algebraic, including a common generalization of Vistoli's Hilbert stack and the stack of branchvarieties of Alexeev and Knutson.19 pagesAlgebraic Geometry14A20; 14C05text