Classifying Infinity Topoi via Weighted Limits

TL;DR

This paper develops a method to classify infinity topoi using weighted limits in the $( abla,2)$-category, demonstrating the existence of classifying topoi for various prestacks including spectra.

Contribution

It introduces the construction of classifying $ abla$-topoi via weighted limits, expanding the understanding of the structure of infinity topoi.

Findings

The $( abla,2)$-category of topoi admits weighted limits.

Several prestacks, such as spectra, have associated classifying topoi.

The framework generalizes the classification of topoi in higher category theory.

Abstract

We construct classifying $\infty$-topoi by showing that the $(\infty,2)$-category of topoi has weighted limits. We show that several prestacks of interest have a classifying topos, including the prestack of spectra.