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

Abstract

We prove that the category of (strictly unital) \(\text{ A}_{\infty }\)-categories, linear over a commutative ring R, with strict \(\text{ A}_{\infty }\)-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 \(\text{ A}_{\infty }\)-categories (resp. resolutions) are cofibrant objects (resp. resolution) in this model structure.