Parametrized higher category theory II: Universal constructions

TL;DR

This paper extends fundamental concepts in $$-category theory to parametrized settings, enabling more flexible and universal constructions within higher category theory.

Contribution

It introduces parametrized versions of key $$-category concepts such as factorization systems, fibrations, and universal constructions, broadening the theoretical framework.

Findings

Develops parametrized factorization systems

Constructs universal Ind and $P^$-constructions

Provides tools for flexible higher categorical analysis

Abstract

We develop parametrized generalizations of a number of fundamental concepts in the theory of $\infty$-categories, including factorization systems, free fibrations, exponentiable fibrations, relative colimits and relative Kan extensions, filtered and sifted diagrams, and the universal constructions Ind and $P^\Sigma$.