fact: Definition is_z_iso_disp_cartesian_factorisation {C : category} {D : disp_cat C} {w x y : C} {f : w --> x} (Hf : is_z_isomorphism f) (fiso := (f ,, Hf) : z_iso w x) {g : x --> y} (Hg : is_z_isomorphism g) (giso := (g ,, Hg) : z_iso x y) {ww : D w} {xx : D x} {yy : D y} {gg : xx -->[ g ] yy} (Hgg : is_cartesian gg) (hh : ww -->[ f · g ] yy) (Hhh : is_z_iso_disp (z_iso_comp fiso giso) hh) : is_z_iso_disp fiso (cartesian_factorisation Hgg f hh).
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Categories.HSET.Univalence UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Presheaf UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Examples.Opposite