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fix(category_theory/limits): adding Type annotations in preserves.lean
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semorrison authored and digama0 committed Dec 2, 2018
1 parent 74b65e2 commit af6ee09
Showing 1 changed file with 12 additions and 12 deletions.
24 changes: 12 additions & 12 deletions category_theory/limits/preserves.lean
Expand Up @@ -46,19 +46,19 @@ with the above definition of "preserves limits".
-/

class preserves_limit (K : J ⥤ C) (F : C ⥤ D) :=
class preserves_limit (K : J ⥤ C) (F : C ⥤ D) : Type (max u₁ u₂ v) :=
(preserves : Π {c : cone K}, is_limit c → is_limit (F.map_cone c))
class preserves_colimit (K : J ⥤ C) (F : C ⥤ D) :=
class preserves_colimit (K : J ⥤ C) (F : C ⥤ D) : Type (max u₁ u₂ v) :=
(preserves : Π {c : cocone K}, is_colimit c → is_colimit (F.map_cocone c))

@[class] def preserves_limits_of_shape (J : Type v) [small_category J] (F : C ⥤ D) :=
@[class] def preserves_limits_of_shape (J : Type v) [small_category J] (F : C ⥤ D) : Type (max u₁ u₂ v) :=
Π {K : J ⥤ C}, preserves_limit K F
@[class] def preserves_colimits_of_shape (J : Type v) [small_category J] (F : C ⥤ D) :=
@[class] def preserves_colimits_of_shape (J : Type v) [small_category J] (F : C ⥤ D) : Type (max u₁ u₂ v) :=
Π {K : J ⥤ C}, preserves_colimit K F

@[class] def preserves_limits (F : C ⥤ D) :=
@[class] def preserves_limits (F : C ⥤ D) : Type (max u₁ u₂ (v+1)) :=
Π {J : Type v} {𝒥 : small_category J}, by exactI preserves_limits_of_shape J F
@[class] def preserves_colimits (F : C ⥤ D) :=
@[class] def preserves_colimits (F : C ⥤ D) : Type (max u₁ u₂ (v+1)) :=
Π {J : Type v} {𝒥 : small_category J}, by exactI preserves_colimits_of_shape J F

instance preserves_limit_of_preserves_limits_of_shape (F : C ⥤ D)
Expand Down Expand Up @@ -122,19 +122,19 @@ Note that again we do not assume a priori that D actually has any
limits.
-/

class reflects_limit (K : J ⥤ C) (F : C ⥤ D) :=
class reflects_limit (K : J ⥤ C) (F : C ⥤ D) : Type (max u₁ u₂ v) :=
(reflects : Π {c : cone K}, is_limit (F.map_cone c) → is_limit c)
class reflects_colimit (K : J ⥤ C) (F : C ⥤ D) :=
class reflects_colimit (K : J ⥤ C) (F : C ⥤ D) : Type (max u₁ u₂ v) :=
(reflects : Π {c : cocone K}, is_colimit (F.map_cocone c) → is_colimit c)

@[class] def reflects_limits_of_shape (J : Type v) [small_category J] (F : C ⥤ D) :=
@[class] def reflects_limits_of_shape (J : Type v) [small_category J] (F : C ⥤ D) : Type (max u₁ u₂ v) :=
Π {K : J ⥤ C}, reflects_limit K F
@[class] def reflects_colimits_of_shape (J : Type v) [small_category J] (F : C ⥤ D) :=
@[class] def reflects_colimits_of_shape (J : Type v) [small_category J] (F : C ⥤ D) : Type (max u₁ u₂ v) :=
Π {K : J ⥤ C}, reflects_colimit K F

@[class] def reflects_limits (F : C ⥤ D) :=
@[class] def reflects_limits (F : C ⥤ D) : Type (max u₁ u₂ (v+1)) :=
Π {J : Type v} {𝒥 : small_category J}, by exactI reflects_limits_of_shape J F
@[class] def reflects_colimits (F : C ⥤ D) :=
@[class] def reflects_colimits (F : C ⥤ D) : Type (max u₁ u₂ (v+1)) :=
Π {J : Type v} {𝒥 : small_category J}, by exactI reflects_colimits_of_shape J F

instance reflects_limit_of_reflects_limits_of_shape (K : J ⥤ C) (F : C ⥤ D)
Expand Down

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