A Model Structure on the Category of $$\text{ A}_{\infty }$$-Categories with Strict Morphisms

We prove that the category of (strictly unital) A∞-categories, linear over a commutative ring
R, with strict A∞-morphisms has a cofibrantly generated model structure. In this model
structure every object is fibrant and the cofibrant objects have cofibrant morphisms. As a
consequence we prove that the semi-free A∞-categories (resp. resolutions) are cofibrant
objects (resp. resolution) in this model structure.