Definition Sum_of_Signatures (S : I -> Signature C D D') : Signature C D D'. Proof. use tpair. - apply H; intro i. apply (S i). - exists (θ (λ i, S i) (λ i, theta (S i))). split. + apply SumStrength1'; intro i; apply (Sig_strength_law1 (S i)). + apply SumStrength2'; intro i; apply (Sig_strength_law2 (S i)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.PointedFunctors. Require Import UniMath.CategoryTheory.PointedFunctorsComposition. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.SubstitutionSystems.Notation. Require Import UniMath.CategoryTheory.Chains.Chains. Require Import UniMath.CategoryTheory.Chains.OmegaCocontFunctors. Require Import UniMath.CategoryTheory.Limits.Products.