t-structures and Barr exactness

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.