Reconstruction of the stacky approach to de Rham cohomology

TL;DR

This paper employs Tannakian reconstruction techniques to connect the stacky approach to de Rham cohomology with classical algebraic de Rham cohomology, providing a conceptual bridge between the two frameworks.

Contribution

It introduces a method to reconstruct the stacky de Rham cohomology from classical algebraic de Rham cohomology using the adjoint functor theorem.

Findings

Reconstruction of the stacky approach from classical theory

Application of Tannakian techniques to de Rham cohomology

Use of adjoint functor theorem in cohomology reconstruction

Abstract

In this short paper, we use Tannakian reconstruction techniques to prove a result that explains how to reconstruct the stacky approach to de Rham cohomology from the classical theory algebraic de Rham cohomology via an application of the adjoint functor theorem.