# A Generalized Blakers-Massey Theorem

## TL;DR

This paper generalizes the Blakers-Massey connectivity theorem to higher toposes and arbitrary modalities, extending classical results and recent work using a proof inspired by Homotopy Type Theory.

## Contribution

It introduces a broad generalization of the classical theorem applicable in higher toposes with arbitrary modalities, unifying and extending previous results.

## Key findings

- Generalized Blakers-Massey theorem proven in higher toposes
- Applicable to arbitrary modalities and factorization systems
- Provides a new proof inspired by Homotopy Type Theory

## Abstract

We prove a generalization of the classical connectivity theorem of Blakers-Massey, valid in an arbitrary higher topos and with respect to an arbitrary modality, that is, a factorization system (L,R) in which the left class is stable by base change. We explain how to rederive the classical result, as well as a recent generalization by Chach\'olski-Scherer-Werndli. Our proof is inspired by the one given in Homotopy Type Theory.