Tannakization of quasi-categories and monadic descent
Romie Banerjee

TL;DR
This paper develops a framework connecting symmetric monoidal stable $$-categories, derived group schemes, and monadic descent, providing new insights into automorphism groups and descent theory in higher category contexts.
Contribution
It introduces a Tannakian formalism for quasi-categories, relating automorphism group schemes to monads via descent under finiteness conditions.
Findings
Constructed derived group schemes from fiber functors.
Established a comparison between representations of the group scheme and descent categories.
Provided conditions under which the comparison functor is an equivalence.
Abstract
Given a symmetric monoidal stable -category and a left adjoint symmetric monoidal fiber functor to for some -ring , one can construct a derived group scheme of monoidal automorphisms of this functor. The left adjoint fiber functor also induces a monad on . Under some finiteness hypothesis on the fiber functor, we show there is a comparison functor from the category of representations of to the descent category of the induced monad on .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra
