Infinity-categorical universal properties of quotients and localizations of A-infinity-categories

TL;DR

This paper demonstrates that specific A-infinity-categorical constructions, including quotients and localizations, satisfy universal properties within the infinity-category framework, with applications to symplectic geometry and a conjecture of Teleman.

Contribution

It establishes that certain models for quotients and localizations of A-infinity categories fulfill universal properties in the infinity-category setting.

Findings

Models for quotients satisfy universal properties.

Models for localizations satisfy universal properties.

Applications to Liouville geometry and Teleman's conjecture.

Abstract

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.