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InfinityCosmos.ForMathlib.CategoryTheory.Bicategory.Strict.Closed

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def CategoryTheory.Bicategory.HomWhiskerLeft (C : Type u) [Bicategory C] (X : C) {Y Y' : C} (g : Y ⟶ Y') :
Functor (X ⟶ Y) (X ⟶ Y')

The morphism (X ⟶ Y) ⥤ (X ⟶ Y') induced by a morphism Y ⟶ Y'.

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    @[simp]
    theorem CategoryTheory.Bicategory.HomWhiskerLeft_obj (C : Type u) [Bicategory C] (X : C) {Y Y' : C} (g : Y ⟶ Y') (f : X ⟶ Y) :
    (HomWhiskerLeft C X g).obj f = CategoryStruct.comp f g
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    @[simp]
    theorem CategoryTheory.Bicategory.HomWhiskerLeft_map (C : Type u) [Bicategory C] (X : C) {Y Y' : C} (g : Y ⟶ Y') {X✝ Y✝ : X ⟶ Y} (φ : X✝ ⟶ Y✝) :
    (HomWhiskerLeft C X g).map φ = whiskerRight φ g
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    def CategoryTheory.Bicategory.HomWhiskerRight (C : Type u) [Bicategory C] {X X' : C} (Y : C) (f : X ⟶ X') :
    Functor (X' ⟶ Y) (X ⟶ Y)
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      @[simp]
      theorem CategoryTheory.Bicategory.HomWhiskerRight_obj (C : Type u) [Bicategory C] {X X' : C} (Y : C) (f : X ⟶ X') (g : X' ⟶ Y) :
      (HomWhiskerRight C Y f).obj g = CategoryStruct.comp f g
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      @[simp]
      theorem CategoryTheory.Bicategory.HomWhiskerRight_map (C : Type u) [Bicategory C] {X X' : C} (Y : C) (f : X ⟶ X') {X✝ Y✝ : X' ⟶ Y} (φ : X✝ ⟶ Y✝) :
      (HomWhiskerRight C Y f).map φ = whiskerLeft f φ
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      def CategoryTheory.Bicategory.HomFunctor (C : Type u) [Bicategory C] [Strict C] :
      Functor Cᵒᵖ (Functor C Cat)
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        class CategoryTheory.Bicategory.Strict.CartesianMonoidal (C : Type u) [Bicategory C] [Strict C] extends CategoryTheory.CartesianMonoidalCategory C :
        Type (max (max u v) w)
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          class CategoryTheory.Bicategory.Strict.CartesianClosed (C : Type u) [Bicategory C] [Strict C] extends CategoryTheory.Bicategory.Strict.CartesianMonoidal C, CategoryTheory.MonoidalClosed C :
          Type (max (max u v) w)
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