Differential graded algebras, or categories, are easy to construct but the information in them is implicit. A-infinity algebras, or categories, are hard to construct but the information in them is more explicit. In this talk I'll present a new point of view on the process of constructing an A-infinity model of a particular differential graded category, the category of matrix factorisations, which emphasises the role of A-infinity idempotents and Atiyah classes. In contrast to earlier work of Seidel, Dyckerhoff, Efimov, Sheridan and Tu in this context, which has focused on the standard generator and its endomorphism algebra, we care about all objects and potentials over arbitrary base rings.