diff --git a/Mathlib/CategoryTheory/GlueData.lean b/Mathlib/CategoryTheory/GlueData.lean
index 5ee2c9f5bf8cc..e274dd3c6f210 100644
--- a/Mathlib/CategoryTheory/GlueData.lean
+++ b/Mathlib/CategoryTheory/GlueData.lean
@@ -232,13 +232,13 @@ theorem types_π_surjective (D : GlueData (Type*)) : Function.Surjective D.π :=
   (epi_iff_surjective _).mp inferInstance
 #align category_theory.glue_data.types_π_surjective CategoryTheory.GlueData.types_π_surjective
 
-theorem types_ι_jointly_surjective (D : GlueData (Type*)) (x : D.glued) :
+theorem types_ι_jointly_surjective (D : GlueData (Type v)) (x : D.glued) :
     ∃ (i : _) (y : D.U i), D.ι i y = x := by
   delta CategoryTheory.GlueData.ι
   simp_rw [← Multicoequalizer.ι_sigmaπ D.diagram]
   rcases D.types_π_surjective x with ⟨x', rfl⟩
   --have := colimit.isoColimitCocone (Types.coproductColimitCocone _)
-  rw [← show (colimit.isoColimitCocone (Types.coproductColimitCocone _)).inv _ = x' from
+  rw [← show (colimit.isoColimitCocone (Types.coproductColimitCocone.{v, v} _)).inv _ = x' from
       ConcreteCategory.congr_hom
         (colimit.isoColimitCocone (Types.coproductColimitCocone _)).hom_inv_id x']
   rcases (colimit.isoColimitCocone (Types.coproductColimitCocone _)).hom x' with ⟨i, y⟩
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Types.lean b/Mathlib/CategoryTheory/Limits/Shapes/Types.lean
index cb36e9416e548..4dfee874d17aa 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Types.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Types.lean
@@ -438,7 +438,7 @@ end UnivLE
 
 /-- The category of types has `Σ j, f j` as the coproduct of a type family `f : J → Type`.
 -/
-def coproductColimitCocone {J : Type u} (F : J → Type u) :
+def coproductColimitCocone {J : Type v} (F : J → TypeMax.{v, u}) :
     Limits.ColimitCocone (Discrete.functor F) where
   cocone :=
     { pt := Σj, F j
@@ -451,19 +451,19 @@ def coproductColimitCocone {J : Type u} (F : J → Type u) :
 #align category_theory.limits.types.coproduct_colimit_cocone CategoryTheory.Limits.Types.coproductColimitCocone
 
 /-- The categorical coproduct in `Type u` is the type theoretic coproduct `Σ j, F j`. -/
-noncomputable def coproductIso {J : Type u} (F : J → Type u) : ∐ F ≅ Σj, F j :=
+noncomputable def coproductIso {J : Type v} (F : J → TypeMax.{v, u}) : ∐ F ≅ Σj, F j :=
   colimit.isoColimitCocone (coproductColimitCocone F)
 #align category_theory.limits.types.coproduct_iso CategoryTheory.Limits.Types.coproductIso
 
 @[elementwise (attr := simp)]
-theorem coproductIso_ι_comp_hom {J : Type u} (F : J → Type u) (j : J) :
+theorem coproductIso_ι_comp_hom {J : Type v} (F : J → TypeMax.{v, u}) (j : J) :
     Sigma.ι F j ≫ (coproductIso F).hom = fun x : F j => (⟨j, x⟩ : Σj, F j) :=
   colimit.isoColimitCocone_ι_hom (coproductColimitCocone F) ⟨j⟩
 #align category_theory.limits.types.coproduct_iso_ι_comp_hom CategoryTheory.Limits.Types.coproductIso_ι_comp_hom
 
 -- porting note: was @[elementwise (attr := simp)], but it produces a trivial lemma
 -- removed simp attribute because it seems it never applies
-theorem coproductIso_mk_comp_inv {J : Type u} (F : J → Type u) (j : J) :
+theorem coproductIso_mk_comp_inv {J : Type v} (F : J → TypeMax.{v, u}) (j : J) :
     (↾fun x : F j => (⟨j, x⟩ : Σj, F j)) ≫ (coproductIso F).inv = Sigma.ι F j :=
   rfl
 #align category_theory.limits.types.coproduct_iso_mk_comp_inv CategoryTheory.Limits.Types.coproductIso_mk_comp_inv