fact: Definition doublecategory := ∑ C:predoublecategory, (has_homsets (und_ob_hor_precategory C) × has_sq_hor_homsets C).
imports: UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Notations UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence