2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70901We show that every 'conveniently Hoelder' homomorphism between Lie groups in the sense of convenient differential calculus is smooth (in the convenient sense). In particular, every Lip^0 homomorphism is smooth.25 pages, LaTeX; v2: minor improvements, typos correctedGroup Theory22E65 (Primary) 26E15, 26E20, 46T20, 58C20 (Secondary)text