A {B C} (f g : B $-> C) : grp_iso_ab_tensor_prod_coeq_l A f g $o ab_coeq_in $== fmap01 ab_tensor_prod A ab_coeq_in. Proof. snrapply ab_tensor_prod_ind_homotopy. reflexivity. Defined.
Require Import Basics.Overture Basics.Tactics. Require Import Types.Forall Types.Sigma Types.Prod. Require Import WildCat.Core WildCat.Equiv WildCat.Monoidal WildCat.Bifunctor. Require Import WildCat.NatTrans WildCat.MonoidalTwistConstruction. Require Import Algebra.Groups.Group Algebra.Groups.QuotientGroup. Require Import Algebra.AbGroups.AbelianGroup Algebra.AbGroups.Biproduct. Require Import Algebra.AbGroups.AbHom Algebra.AbGroups.FreeAbelianGroup. Require Import Algebra.AbGroups.Abelianization Algebra Algebra.Groups.FreeGroup. Require Import Colimits.Quotient. Require Import Spaces.List.Core Spaces.Int. Require Import AbGroups.Z. Require Import Truncations.