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7 changes: 4 additions & 3 deletions Mathlib/CategoryTheory/Limits/VanKampen.lean
Original file line number Diff line number Diff line change
Expand Up @@ -686,9 +686,10 @@ theorem isVanKampenColimit_extendCofan {n : ℕ} (f : Fin (n + 1) → C)
· simp only [Fin.cases_zero, m₁]
· simp only [← m₂, colimit.ι_desc_assoc, Discrete.functor_obj,
Cofan.mk_pt, Cofan.mk_ι_app, Fin.cases_succ]
induction' j using Fin.inductionOn with j _
· exact t₂' ⟨WalkingPair.left⟩
· have t₁' := (t₁ (Cofan.mk _ (Sigma.ι fun (j : Fin n) ↦ F.obj ⟨j.succ⟩)) (Discrete.natTrans
induction j using Fin.inductionOn with
| zero => exact t₂' ⟨WalkingPair.left⟩
| succ j _ =>
have t₁' := (t₁ (Cofan.mk _ (Sigma.ι fun (j : Fin n) ↦ F.obj ⟨j.succ⟩)) (Discrete.natTrans
fun i ↦ α.app _) (Sigma.desc (fun j ↦ α.app _ ≫ c₁.inj _)) ?_
(NatTrans.equifibered_of_discrete _)).mp ⟨coproductIsCoproduct _⟩ ⟨j⟩
rotate_left
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