Deformations theory and minimal models of operads for Nijenhuis algebras morphisms

In this paper, we introduce a new cohomology theory related to deformations of Nijenhuis algebra morphisms, which involves simultaneous deformations of two Nijenhuis algebras and of a morphism between them. This framework interprets the lower-degree cohomology groups in terms of formal deformations. Moreover, we prove that the cohomology of a morphism of Nijenhuis algebras is isomorphic to the cohomology of an auxiliary Nijenhuis algebra. Finally, we construct a minimal model for the operad governing Nijenhuis algebras morphisms.