The category of strictly unital A∞-categories with strict morphisms admits a cofibrantly generated model structure with quasi-equivalences as weak equivalences.
Localizations of the categories of A∞-categories and Internal Homs
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A model structure on the category of A$_\infty$-categories with strict morphisms
The category of strictly unital A∞-categories with strict morphisms admits a cofibrantly generated model structure with quasi-equivalences as weak equivalences.