1 citations · 2 across the 8 of their papers we have counts for
8 papers
Categorification of sheaf theory
Germán Stefanich
We discuss a systematic procedure for categorifying presentable six-functor formalisms. Our main result produces, given the input of a representation of the -category of co…
Dualizability of derived categories of algebraic stacks
Germán Stefanich
We show that, for a Noetherian algebraic stack with quasi-affine diagonal , the stable -category of quasi-coherent sheaves on is dualizable if and only if the reduce…
Report on -descendability
Benjamin Antieau, Germán Stefanich
We introduce the notion of -descendability as well as a derived variant. We prove that several classes of descendable maps of commutative rings are $\mathbb{E}_\…
Tannaka duality and 1-affineness
Germán Stefanich
We show that Lurie's results on Tannaka duality for geometric stacks hold without any tameness hypotheses. We deduce this as a consequence of an affineness theorem in the theory of…
Derived -categories as exact completions
Germán Stefanich
We develop the theory of exact completions of regular -categories, and show that the -categorical exact completion (resp. hypercompletion) of an abelian category re…
Classification of fully dualizable linear categories
Germán Stefanich
We prove that if is a G-ring then every fully dualizable -linear cocomplete category is equivalent to a twist by a -gerbe of the category of modules over a fin…
Presentable -categories
Germán Stefanich
We define for each a symmetric monoidal -category whose objects we call presentable -categories, generalizing the usual theor…
Higher sheaf theory I: Correspondences
Germán Stefanich
We prove a universal property for the -category of correspondences, generalizing and providing a new proof for the case from [GR17]. We also provide conditions…