For two Banach algebras A and B and a non-zero multiplicative linear functional θ on B, Monfared introduced the θ−Lau product structure A ×θ B. In this paper, we investigate and study the notions of φ−biprojectivity, φ−biflatness and φ−Johnson amenability of A ×θ B and their relation with A and B. As an application, we characterize φ-biflatness, φ-biprojectivity and φ-Johnson amenability for θ−Lau product of Banach algebras related to locally compact groups and discrete semigroups
