fact: Definition is_iso_twosided_disp {C₁ C₂ : category} {D : twosided_disp_cat C₁ C₂} {x₁ x₂ : C₁} {y₁ y₂ : C₂} {xy₁ : D x₁ y₁} {xy₂ : D x₂ y₂} {f : x₁ --> x₂} {g : y₁ --> y₂} (Hf : is_z_isomorphism f) (Hg : is_z_isomorphism g) (fg : xy₁ -->[ f ][ g ] xy₂) : UU := let f_z_iso : z_iso x₁ x₂ := f ,, Hf in let g_z_iso : z_iso y₁ y₂ := g ,, Hg in ∑ (gf : xy₂ -->[ inv_from_z_iso f_z_iso ][ inv_from_z_iso g_z_iso ] xy₁), (fg ;;2 gf = transportb_disp_mor2 (z_iso_inv_after_z_iso f_z_iso) (z_iso_inv_after_z_iso g_z_iso) (id_two_disp _)) × (gf ;;2 fg = transportb_disp_mor2 (z_iso_after_z_iso_inv f_z_iso) (z_iso_after_z_iso_inv g_z_iso) (id_two_disp _)).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat