Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Orateur(s) Mattia ORNAGHI - Ben Gurion University,
Titre Localizations of the category of $A_{\infty}$-categories and Internal Homs
Horaire14:00 à 15:00

In the first part of the talk, we prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital $A_\infty$-categories with respect to the corresponding classes of quasi-equivalences are all equivalent. As an application, in the second part, we give a complete proof of a claim by Kontsevich stating that the category of internal Homs for two dg categories can be described as the category of strictly unital $A_\infty$-functors between them. This is a joint work with Prof. A. Canonaco and Prof. P. Stellari arXiv:1811.07830.