proposition: Lemma filtered_alt_has_discrete_cocones {J : category} (filtalt : is_filtered_alt J) (X : UU) (d : diagram (discrete_graph X) J) (n : nat) (w : X ≃ ⟦ n ⟧) : ∃ z : J, cocone d z.
proof: Proof. use(filtered_alt_has_discrete_cocones_stn filtalt n). - exact(make_discrete_diagram (λ k : ⟦ n ⟧, dob d (invmap w k))). - intros [P Pcc]; apply hinhpr. exists P. use make_discrete_cocone. + intro x. apply(transportf (fun y : X => J⟦ dob d y, P ⟧) (homotinvweqweq w x)). exact(coconeIn Pcc (w x)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.covyoneda UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.FiniteSets UniMath.CategoryTheory.Limits.StandardDiagrams