Homotopical exact squares and derivators

TL;DR

This paper generalizes the concept of exact squares within a homotopical framework and explores its connection to the theory of derivators, advancing the understanding of categorical structures in homotopy theory.

Contribution

It introduces a homotopical generalization of exact squares and clarifies their relationship with derivators, enriching the theoretical foundation of homotopy categorical structures.

Findings

Established a homotopical version of exact squares

Linked the generalized notion to derivator theory

Provided insights into categorical structures in homotopy theory

Abstract

The aim of this paper is to generalize in a homotopical framework the notion of exact square introduced by Ren\'e Guitart, and explain the relationship between this generalization and the theory of derivators.