  We show that certain hands-on A-infinity-categorical constructions satisfy
desirable universal properties in the infinity-category of A-infinity
categories. For sufficiently cofibrant A-infinity categories, two models for
quotients of A-infinity categories (as constructed by Lyubashenko-Manzyuk and
Lyubashenko-Ovisienko), and a model for localizations (as used by
Ganatra-Pardon-Shende), satisfy the relevant universal properties. We apply the
results here in a companion work to prove a Liouville version of a conjecture
of Teleman from the 2014 ICM.
