Tannaka duality and stable infinity-categories
Isamu Iwanari
TL;DR
This paper develops a new framework for understanding symmetric monoidal stable infinity-categories via Tannaka duality, linking them to derived quotient stacks and providing characterization results in characteristic zero.
Contribution
It introduces the concept of fine Tannakian infinity-categories and establishes Tannakian duality results for symmetric monoidal stable infinity-categories over fields of characteristic zero.
Findings
Characterization of symmetric monoidal stable infinity-categories via Tannaka duality
Connection between derived quotient stacks and infinity-categories
Applications to specific examples in the field
Abstract
We introduce a notion of fine Tannakian infinity-categories and prove Tannakian characterization results for symmetric monoidal stable infinity-categories over a field of characteristic zero. It connects derived quotient stacks with symmetric monoidal stable infinity-categories which satisfy a certain simple axiom. We also discuss several applications to examples.
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