t-structures and Barr exactnessMPIM

by Gérman Stefanich

Monday Jan 27, 2025, 11:00 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Abstract homotopy theory seminar 

A classical theorem of Tierney characterizes abelian categories as those additive categories which satisfy a further purely nonadditive property known as Barr exactness. In this talk I will explain a version of this result in the setting of higher category theory: an infinity category is Barr exact and additive if and only if it arises as the connective half of a t-structure on some stable infinity category. From this perspective, we will reinterpret the procedure of deriving an abelian category A as an instance of the classical procedure of exact completion; concretely, this identifies the connective derived infinity category of A as a natural full subcategory of the infinity topos of sheaves for a certain Grothendieck topology on A.