2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160889We introduce and study non-abelian cohomology sets of Hopf algebras with coefficients in Hopf comodule algebras. We prove that these sets generalize as well Serre's non-abelian group cohomology theory as the cohomological theory constructed by the authors in a previous article. We establish their functoriality and compute explicit examples. Further we classify Hopf torsors.This paper is conceived as the continuation of the article of the same authors entitled "Non-Abelian Hopf Cohomology", J. Algebra t. 312, (2007), no 2, p. 733 -- 754Quantum Algebra(Primary) 18G50, 16W30, 14A22; (Secondary) 20J06, 55U10text