proposition: Lemma scalar_extension_terminal_iso_is_iso : is_inverse_in_precat (C := HSET) scalar_extension_terminal_iso_mor scalar_extension_terminal_iso_inv.
proof: Proof. split. - use funextfun. intro x. use (issurjsetquotpr _ x (_ ,, isasetsetquot _ _ _) _). intro y. refine (!maponpaths _ (pr2 y) @ _ @ pr2 y). apply iscompsetquotpr. apply eqrel_impl. apply hinhpr. exists (pr1 (element_is_terminal (pr21 y))). split. + apply iscontrunit. + exact (!pr2 (element_is_terminal _)). - use funextfun. intro t. exact (!pr2 iscontrunit _). 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