Lemma skewMonoid_composition_laws {T T' T'' : skewMonoid_data } (α : skewMonoid_Mor T T') (α' : skewMonoid_Mor T' T'') : skewMonoid_Mor_laws (α · α'). Proof. split; intros; simpl. - rewrite assoc. set (H:=skewMonoid_Mor_μ α ); simpl in H. rewrite H; clear H; rewrite <- !assoc. set (H:=skewMonoid_Mor_μ α' ); simpl in H. etrans;[apply cancel_precomposition,H|]. clear H. etrans;[apply assoc|]. apply cancel_postcomposition. apply pathsinv0. apply (functor_comp tensor (_ #, _) (_ #, _)). - rewrite assoc. eapply pathscomp0; [apply cancel_postcomposition, skewMonoid_Mor_η|]. apply skewMonoid_Mor_η. Qed.
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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.SkewMonoidal.SkewMonoidalCategories.