2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72842We propose a detailed systematic study of a group H^2_L(A) associated, by elementary means of lazy 2-cocycles, to any Hopf algebra A. This group was introduced by Schauenburg (with a different name) in order to generalize G.I. Kac's exact sequence. We study the various interplays of lazy cohomology in Hopf algebra theory: Galois and biGalois objects, Brauer groups and projective representations. We obtain a Kac-Schauenburg-type sequence for double crossed products of possibly infinite-dimensional Hopf algebras. Finally the explicit computation of H^2_L(A) for monomial Hopf algebras and for a class of cotriangular Hopf algebras is performed.Reference to Schauenburg's work is added. Section 4 is improved using a Kac-Schauenburg-type exact sequenceQuantum Algebra16W30; 18D10text