  We prove, over any base ring, that the infinity-category of strictly unital
A-infinity-categories (and strictly unital functors) is equivalent to the
infinity-category of unital A-infinity-categories (and unital functors). We
also identify various models for internal homs and mapping spaces in the
infinity-categories of dg-categories and of A-infinity--categories,
generalizing results of To\"en and Faonte.
