Cut systems and matrix factorisations I

The bicategory of Landau-Ginzburg models has polynomials as objects and matrix factorisations as $1$-morphisms. The composition of these $1$-morphisms produces infinite rank matrix factorisations, which is a nuisance. In this paper we define an equivalent bicategory in which composition of $1$-morphisms produces finite rank matrix factorisations equipped with the action of a Clifford algebra.