proposition: Proposition comm_nat_z_iso_ob {w x y z : C} (f : x --> w) (g : y --> w) (h : z --> y) (k : z --> x) (p : k · f = h · g) (F := fiber_functor_from_cleaving D HD f : D[{w}] ⟶ D[{x}]) (G := fiber_functor_from_cleaving D HD g : D[{w}] ⟶ D[{y}]) (H := fiber_functor_from_cleaving D HD h : D[{y}] ⟶ D[{z}]) (K := fiber_functor_from_cleaving D HD k : D[{x}] ⟶ D[{z}]) (φ : D[{w}]) : comm_nat_z_iso f g h k p φ = fiber_functor_from_cleaving_comp _ _ _ φ · fiber_functor_on_eq HD p φ · fiber_functor_from_cleaving_comp_inv _ _ _ φ.
proof: Proof. apply assoc. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Pullbacks