Definition exp_functor (lt : list sort × sort) : functor sortToC2 sortToCC. Proof. induction lt as [l t]. use (list_ind _ _ _ l); clear l. - exact (post_comp_functor (projSortToC t)). - intros s l _. exact (pre_comp_functor (option_list (cons s l)) ∙ post_comp_functor (projSortToC t)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Combinatorics.Lists. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Chains.All. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.SubstitutionSystems.SumOfSignatures. Require Import UniMath.SubstitutionSystems.BinProductOfSignatures. Require Import UniMath.SubstitutionSystems.SignatureExamples. Require Import UniMath.SubstitutionSystems.MultiSortedBindingSig.