Tannakization of quasi-categories and monadic descent

2016/08/03 by Romie Banerjee, Banerjee, Romie
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1608.01148

openalex publication_date 2016/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a symmetric monoidal stable ∞-category C and a left adjoint symmetric monoidal fiber functor to Mod_A^⊗ for some 𝔼_∞-ring A, one can construct a derived group scheme G of monoidal automorphisms of this functor. The left adjoint fiber functor also induces a monad on C. Under some finiteness hypothesis on the fiber functor, we show there is a comparison functor from the category of representations of G to the descent category of the induced monad on C.

Citations

• Some Higher Coalgebra

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