Monoidal Infinity Category of Complexes from Tannakian Viewpoint

TL;DR

This paper establishes a derived Tannaka duality for algebraic stacks, showing that morphisms correspond to symmetric monoidal functors between their associated stable infinity-categories of complexes, enabling reconstruction of stacks.

Contribution

It introduces a derived analogue of Tannaka duality, linking morphisms of schemes or stacks to monoidal functors between their infinity-categories of complexes.

Findings

Morphisms correspond to symmetric monoidal functors between infinity-categories.

Algebraic stacks can be reconstructed from their complexes under certain conditions.

Provides a new perspective on the relationship between stacks and their derived categories.

Abstract

In this paper we prove that a morphism between schemes or stacks naturally corresponds to a symmetric monoidal functor between stable infinity-categories of quasi-coherent complexes. It can be viewed as a derived analogue of Tannaka duality. As a consequence, we deduce that an algebraic stack satisfying a certain condition can be recovered from the stable infinity-category of quasi-coherent complexes with tensor operation.