Definition inserter_cone_functor_data (cone : inserter_cone) (x : B) : functor_data (hom x cone) (dialgebra (post_comp x f) (post_comp x g)). Proof. use make_functor_data. - exact (λ h, h · inserter_cone_pr1 cone ,, rassociator _ _ _ • (h ◃ inserter_cone_cell cone) • lassociator _ _ _). - refine (λ x y g, g ▹ _ ,, _) ; cbn. abstract (rewrite !vassocr ; rewrite rwhisker_rwhisker_alt ; rewrite !vassocl ; apply maponpaths ; rewrite !vassocr ; rewrite vcomp_whisker ; rewrite !vassocl ; apply maponpaths ; rewrite rwhisker_rwhisker ; apply idpath). 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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.Categories.Dialgebras. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms.