Flat functors in the context of fibration categories

TL;DR

This paper explores the relationship between flat functors in higher category theory and exact functors in fibration categories, providing a method to approximate one by the other and confirming a key equivalence between their associated categories.

Contribution

It introduces a procedure to approximate flat $ abla$-functors by exact functors, bridging finitely complete quasicategories and fibration categories.

Findings

Established a method to approximate flat $ abla$-functors with exact functors.

Reproved the DK-equivalence between fibration categories and finitely complete quasicategories.

Abstract

We investigate the connection between left exact $\infty$-functors between finitely complete quasicategories and exact functors between fibration categories, describing a procedure to approximate flat $\infty$-functors of the former type by exact functors of the latter type. As an application, we recover a proof of the DK-equivalence between the relative category of fibration categories and that of finitely complete quasicategories.