A Model Independent Universal Property for the Lax 2-Functor Classifier

TL;DR

This paper introduces a model-independent definition of lax 2-functors within $( abla,2)$-category theory, aligning with existing combinatorial models used in derived algebraic geometry.

Contribution

It provides a new, model-independent framework for lax 2-functors that matches established combinatorial models in higher category theory.

Findings

Defines a model-independent concept of lax 2-functors.

Shows equivalence with existing combinatorial models.

Facilitates applications in derived algebraic geometry.

Abstract

In this article we provide a model-independent definition of the concept of lax $2$-functors from $(\infty,2)$-category theory and show that it agrees with the existing and widely used combinatorial model for those in terms of inert-cocartesian functors, which is utilized for example in the foundational work of Gaitsgory and Rozenblyum on Derived Algebraic Geometry to talk about the lax Gray tensor product.