Definition homotsec_natural {X Y : UU} {f g : X → Y} (e : f ~ g) {x y : X} (p : x = y) : e x @ maponpaths g p = maponpaths f p @ e y. Proof. induction p. apply pathscomp0rid. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.Core.Examples.TwoType. Require Import UniMath.Bicategories.PseudoFunctors.Examples.ApFunctor.