Higher Tannaka and Beyond

TL;DR

This paper explores the foundations and implications of Higher Tannaka duality, emphasizing the role of Hopf algebras, and introduces new concepts like blow-ups and fractal infinity-categories to advance the reconstruction program for stacks.

Contribution

It reviews Wallbridge's work on Higher Tannaka duality, analyzes its meaning for stack reconstruction, and introduces innovative concepts such as blow-ups and fractal infinity-categories.

Findings

Hopf algebras are crucial for generating Tannakian infinity-categories

Higher Tannaka acts as a reconstruction program for stacks

Introduction of blow-ups and fractal infinity-categories as new tools

Abstract

We consider the origins of Higher Tannaka duality, as well as it consequences. In a first time we review the work of J. Wallbridge on that subject, which shows in particular that Hopf algebras are essential to generating Tannakian infinity-categories. While doing so we provide an analysis of what it means for Higher Tannaka to be a reconstruction program for stacks. Putting Wallbridge's work in perspective paves the way for causal models in Higher Category Theory. We introduce two interesting concepts that we deem to be instrumental within this framework; that of blow-ups of categories as well as that of fractal infinity-categories.