Demonstrates a cofibrantly generated model structure for A∞-categories over a commutative ring, implying outcomes for semi-free A∞-categories.
We prove that the category of (strictly unital) A∞ A ∞ -categories, linear over a commutative ring R , with strict A∞ 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∞ A ∞ -categories (resp. resolutions) are cofibrant objects (resp. resolution) in this model structure.
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Mattia Ornaghi (2026) studied this question.
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