Definition preserves_filtered_colimits {C D : category} (F : functor C D) : UU := ∏ (J : category), is_filtered J -> preserves_colimits_of_shape F J.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.covyoneda. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.FiniteSets. Require Import UniMath.CategoryTheory.Limits.StandardDiagrams.