proposition: Lemma scalar_extension_binproduct_iso_is_morphism : ∏ x m, mor_action_ax (X := (scalar_extension_functor (binproducts_monoid_action_cat M X X'))) (X' := BinProductObject _ (binproducts_monoid_action_cat M' (scalar_extension_functor X) (scalar_extension_functor X'))) scalar_extension_binproduct_iso_mor x m.
proof: Proof. intros x m. use (issurjsetquotpr _ x (_ ,, isasetdirprod _ _ (isasetsetquot _) (isasetsetquot _) _ _)). intro y. now rewrite <- (pr2 y). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Algebra.Monoids UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total