{A B} {f g : A $-> B} {A' B'} {f' g' : A' $-> B'} (a : A $-> A') (b : B $-> B') (p : f' $o a $== b $o f) (q : g' $o a $== b $o g) {A'' B''} {f'' g'' : A'' $-> B''} (a' : A' $-> A'') (b' : B' $-> B'') (p' : f'' $o a' $== b' $o f') (q' : g'' $o a' $== b' $o g') : functor_ab_coeq a' b' p' q' $o functor_ab_coeq a b p q $== functor_ab_coeq (a' $o a) (b' $o b) (hconcat p p') (hconcat q q'). Proof. snrapply ab_coeq_ind_homotopy. simpl; reflexivity. Defined.
Require Import Basics Types. Require Import WildCat HSet Truncations.Core Modalities.ReflectiveSubuniverse. Require Import Groups.QuotientGroup AbelianGroup Biproduct.