Unifying Koszul dualities via point-set models

par Dr Victor Roca i Lucio

mardi 23 juin 2026, 14:00 → 15:00 Europe/Paris

IMT 1R2 207 (Salle Pellos)

The classical bar-cobar adjunction between dg algebras and dg coalgebras goes back to the origins of differential homological algebra as developed by Cartan, Eilenberg, Moore, and many others, and is part of the broader framework of Koszul duality. In recent years, several ∞-categorical analogues of this adjunction have been developed, notably by Lurie, Francis--Gaitsgory, and Heuts. However, there is no comparison in the literature between the classical chain-level constructions and their higher-categorical counterparts, and surprisingly perhaps, the two constructions are not quite compatible.

In this talk, I will explain who to construct a unified framework relating these different forms of Koszul duality in the differential graded setting. Along the way, I will also explain how giving point-set models for ∞-categorical types of coalgebras plays a major role in this story. This talk will be based on two joint works with Dan Petersen and Sinan Yalin.