Cartesian factorization systems and pointed cartesian fibrations of $\infty$-categories

TL;DR

This paper establishes an equivalence between cartesian factorization systems and pointed cartesian fibrations in the context of ategories, extending known results from ordinary categories to higher categories.

Contribution

It generalizes a classical equivalence to ategories, revealing deeper connections between factorization systems and fibrations in higher category theory.

Findings

Proves an equivalence between ategories of cartesian factorization systems and pointed cartesian fibrations.

Extends classical results from ordinary categories to ategories.

Provides new insights into the structure of ategories and their fibrations.

Abstract

The goal of this paper is to prove an equivalence between the $(\infty,2)$-category of cartesian factorization systems of $\infty$-categories and that of pointed cartesian fibrations of $\infty$-categories. This generalizes a similar result known for ordinary categories and sheds some light on the interplay between these two seemingly distant concepts.