Flat functors in the context of fibration categories

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.

arXiv comment41 pages, this document originated from Section 4 of a previous article (arXiv:2509.03371) after corrections and expansions