Flat functors in the context of fibration categories

We investigate the connection between left exact $\mathrm{\infty }$-functors between finitely complete quasicategories and exact functors between fibration categories, describing a procedure to approximate flat $\mathrm{\infty }$-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.