fact: Definition is_filtered_alt (J : category) : UU := ∥ J ∥ × (∏ (d : diagram bool_graph J), ∃ z : J, cocone d z) × (∏ (d : diagram pair_graph J), ∃ z : J, cocone d z).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.covyoneda UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.FiniteSets UniMath.CategoryTheory.Limits.StandardDiagrams