2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103644In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras. We prove a multiplicativity theorem, a denominator theorem, and some conjectures on properties of the mutation graph. As in the previous article, the proofs rely on the Calabi-Yau property of the cluster category.23 pages. The proofs rely on a weaker version of positivityRepresentation TheoryRings and Algebras16G20; 18E30text