proposition: Lemma indexed_set_cat_arrow_is_unique (t : indexed_set_cat ⟦ c, indexed_set_cat_tip ⟧) (Ht : is_cone_mor cc indexed_set_cat_cone t) : t = indexed_set_cat_arrow.
proof: Proof. apply funextsec. intro i. exact (limArrowUnique (component_limit i) (c i) (unindex_cone cc i) (t i) (λ v, (eqtohomot (Ht v) i))). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Univalence UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits