Crossed modules of Cat1-BiHom-associative dialgebras

We develop a theory of crossed modules for BiHom-associative dialgebras. After introducing actions and semidirect products in this category, we define a notion of crossed module adapted to the BiHom setting and characterize it in terms of split extensions. Our main result establishes a categorical equivalence between the category of crossed modules of BiHom-associative dialgebras and the category of Cat1-BiHom-associative dialgebras.