# Homotopies in Grothendieck fibrations

## TL;DR

This paper introduces a 2-categorical structure on the base of Grothendieck fibrations and demonstrates its application to model categories, recovering the classical 2-category of spaces in the case of topological spaces.

## Contribution

It defines a natural 2-categorical structure on the base of Grothendieck fibrations and applies it to model categories, linking fibrations to the 2-category of spaces.

## Key findings

- The construction recovers the 2-category of spaces for Top.
- The framework applies to a large class of Grothendieck fibrations.
- Connects fibrations with homotopy categories in a 2-categorical context.

## Abstract

We define a natural 2-categorical structure on the base category of a large class of Grothendieck fibrations. Given any model category $\mathbf{C}$, we apply this construction to a fibration whose fibers are the homotopy categories of the slice categories $\mathbf{C}/A$, and we show that in the case $\mathbf{C}=\mathbf{Top}$, our construction applied to this fibration recovers the usual 2-category of spaces.