proposition: Lemma ObjectToCoproduct: ∏ (a : stn 1 -> C), Coproduct (stn 1) C a.
proof: Proof. intros a. set (stn1ob := invweq(weqstn1tounit) tt). use (make_Coproduct _ _ _ (a stn1ob)). intros i. exact (idtoiso (! (maponpaths a (isconnectedstn1 stn1ob i)))). use (make_isCoproduct _ _ C). intros c g. use (unique_exists (g stn1ob)). intros i. rewrite <- (isconnectedstn1 stn1ob i). apply id_left. intros y. apply impred_isaprop. intros t. apply C. intros y X. rewrite <- (X stn1ob). apply pathsinv0. apply id_left. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Initial