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3 changes: 2 additions & 1 deletion Mathlib/CategoryTheory/Presentable/Adjunction.lean
Original file line number Diff line number Diff line change
Expand Up @@ -86,8 +86,9 @@ lemma isCardinalLocallyPresentable [IsCardinalLocallyPresentable C κ]
lemma isCardinalAccessibleCategory [IsCardinalAccessibleCategory C κ]
[G.IsCardinalAccessible κ] [G.Full] [G.Faithful] :
IsCardinalAccessibleCategory D κ where
toHasCardinalFilteredColimits := ⟨fun _ _ _ ↦
toHasCardinalFilteredColimits := ⟨fun J _ _ ↦
let : Reflective G := ⟨_, adj⟩
have := HasCardinalFilteredColimits.hasColimitsOfShape C κ J
hasColimitsOfShape_of_reflective G⟩
toHasCardinalFilteredGenerator := adj.hasCardinalFilteredGenerator κ

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12 changes: 5 additions & 7 deletions Mathlib/CategoryTheory/Presentable/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -344,17 +344,15 @@ end

section

variable (C) (κ : Cardinal.{w}) [Fact κ.IsRegular]

/-- A category has `κ`-filtered colimits if it has colimits of shape `J`
for any `κ`-filtered category `J`. -/
class HasCardinalFilteredColimits : Prop where
hasColimitsOfShape (J : Type w) [SmallCategory J] [IsCardinalFiltered J κ] :
class HasCardinalFilteredColimits (C : Type u₁) [Category.{v₁} C]
(κ : Cardinal.{w}) [Fact κ.IsRegular] : Prop where
hasColimitsOfShape (C) (J : Type w) [SmallCategory J] [IsCardinalFiltered J κ] :
HasColimitsOfShape J C := by intros; infer_instance

attribute [instance] HasCardinalFilteredColimits.hasColimitsOfShape

instance [HasColimitsOfSize.{w, w} C] : HasCardinalFilteredColimits.{w} C κ where
instance (κ : Cardinal.{w}) [Fact κ.IsRegular] [HasColimitsOfSize.{w, w} C] :
HasCardinalFilteredColimits.{w} C κ where

end

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Original file line number Diff line number Diff line change
Expand Up @@ -99,6 +99,7 @@ lemma MorphismProperty.isCardinalAccessible_ι_isLocal
W.isLocal.ι.IsCardinalAccessible κ where
preservesColimitOfShape J _ _ := by
have := W.isClosedUnderColimitsOfShape_isLocal J κ hW
have := HasCardinalFilteredColimits.hasColimitsOfShape C κ J
infer_instance

namespace OrthogonalReflection
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