File: Mathlib/CategoryTheory/Functor/Trifunctor.lean

full_name: CategoryTheory.bifunctorComp₁₂Obj
code: /-- Auxiliary definition for `bifunctorComp₁₂`. -/
@[simps]
def bifunctorComp₁₂Obj (X₁ : C₁) : C₂ ⥤ C₃ ⥤ C₄ 
goal: CategoryTheory.Functor C₂ (CategoryTheory.Functor C₃ C₄)

full_name: CategoryTheory.bifunctorComp₁₂Obj_obj_obj
code: /-- Auxiliary definition for `bifunctorComp₁₂`. -/
@[simps]
def bifunctorComp₁₂Obj (X₁ : C₁) : C₂ ⥤ C₃ ⥤ C₄ 
goal: ((CategoryTheory.bifunctorComp₁₂Obj F₁₂ G X₁).obj X₂).obj X₃ = (G.obj ((F₁₂.obj X₁).obj X₂)).obj X₃

full_name: CategoryTheory.bifunctorComp₁₂Obj_map_app
code: /-- Auxiliary definition for `bifunctorComp₁₂`. -/
@[simps]
def bifunctorComp₁₂Obj (X₁ : C₁) : C₂ ⥤ C₃ ⥤ C₄ 
goal: ((CategoryTheory.bifunctorComp₁₂Obj F₁₂ G X₁).map φ).app X₃ = (G.map ((F₁₂.obj X₁).map φ)).app X₃

full_name: CategoryTheory.bifunctorComp₁₂Obj_obj_map
code: /-- Auxiliary definition for `bifunctorComp₁₂`. -/
@[simps]
def bifunctorComp₁₂Obj (X₁ : C₁) : C₂ ⥤ C₃ ⥤ C₄ 
goal: ((CategoryTheory.bifunctorComp₁₂Obj F₁₂ G X₁).obj X₂).map φ = (G.obj ((F₁₂.obj X₁).obj X₂)).map φ

full_name: CategoryTheory.bifunctorComp₁₂
code: /-- Given two bifunctors `F₁₂ : C₁ ⥤ C₂ ⥤ C₁₂` and `G : C₁₂ ⥤ C₃ ⥤ C₄`, this is
the trifunctor `C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄` obtained by composition. -/
@[simps]
def bifunctorComp₁₂ : C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄ 
goal: CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ (CategoryTheory.Functor C₃ C₄))

full_name: CategoryTheory.bifunctorComp₁₂_map_app_app
code: /-- Given two bifunctors `F₁₂ : C₁ ⥤ C₂ ⥤ C₁₂` and `G : C₁₂ ⥤ C₃ ⥤ C₄`, this is
the trifunctor `C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄` obtained by composition. -/
@[simps]
def bifunctorComp₁₂ : C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄ 
goal: (((CategoryTheory.bifunctorComp₁₂ F₁₂ G).map φ).app X₂).app X₃ = (G.map ((F₁₂.map φ).app X₂)).app X₃

full_name: CategoryTheory.bifunctorComp₁₂_obj
code: /-- Given two bifunctors `F₁₂ : C₁ ⥤ C₂ ⥤ C₁₂` and `G : C₁₂ ⥤ C₃ ⥤ C₄`, this is
the trifunctor `C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄` obtained by composition. -/
@[simps]
def bifunctorComp₁₂ : C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄ 
goal: (CategoryTheory.bifunctorComp₁₂ F₁₂ G).obj X₁ = CategoryTheory.bifunctorComp₁₂Obj F₁₂ G X₁

full_name: CategoryTheory.bifunctorComp₂₃Obj_obj_map
code: /-- Auxiliary definition for `bifunctorComp₂₃`. -/
@[simps]
def bifunctorComp₂₃Obj (X₁ : C₁) : C₂ ⥤ C₃ ⥤ C₄ 
goal: ((CategoryTheory.bifunctorComp₂₃Obj F G₂₃ X₁).obj X₂).map φ = (F.obj X₁).map ((G₂₃.obj X₂).map φ)

full_name: CategoryTheory.bifunctorComp₂₃Obj_map_app
code: /-- Auxiliary definition for `bifunctorComp₂₃`. -/
@[simps]
def bifunctorComp₂₃Obj (X₁ : C₁) : C₂ ⥤ C₃ ⥤ C₄ 
goal: ((CategoryTheory.bifunctorComp₂₃Obj F G₂₃ X₁).map φ).app X₃ = (F.obj X₁).map ((G₂₃.map φ).app X₃)

full_name: CategoryTheory.bifunctorComp₂₃Obj
code: /-- Auxiliary definition for `bifunctorComp₂₃`. -/
@[simps]
def bifunctorComp₂₃Obj (X₁ : C₁) : C₂ ⥤ C₃ ⥤ C₄ 
goal: CategoryTheory.Functor C₂ (CategoryTheory.Functor C₃ C₄)

full_name: CategoryTheory.bifunctorComp₂₃Obj_obj_obj
code: /-- Auxiliary definition for `bifunctorComp₂₃`. -/
@[simps]
def bifunctorComp₂₃Obj (X₁ : C₁) : C₂ ⥤ C₃ ⥤ C₄ 
goal: ((CategoryTheory.bifunctorComp₂₃Obj F G₂₃ X₁).obj X₂).obj X₃ = (F.obj X₁).obj ((G₂₃.obj X₂).obj X₃)

full_name: CategoryTheory.bifunctorComp₂₃
code: /-- Given two bifunctors `F : C₁ ⥤ C₂₃ ⥤ C₄` and `G₂₃ : C₂ ⥤ C₃ ⥤ C₄`, this is
the trifunctor `C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄` obtained by composition. -/
@[simps]
def bifunctorComp₂₃ : C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄ 
goal: CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ (CategoryTheory.Functor C₃ C₄))

full_name: CategoryTheory.bifunctorComp₂₃_obj
code: /-- Given two bifunctors `F : C₁ ⥤ C₂₃ ⥤ C₄` and `G₂₃ : C₂ ⥤ C₃ ⥤ C₄`, this is
the trifunctor `C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄` obtained by composition. -/
@[simps]
def bifunctorComp₂₃ : C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄ 
goal: (CategoryTheory.bifunctorComp₂₃ F G₂₃).obj X₁ = CategoryTheory.bifunctorComp₂₃Obj F G₂₃ X₁

full_name: CategoryTheory.bifunctorComp₂₃_map_app_app
code: /-- Given two bifunctors `F : C₁ ⥤ C₂₃ ⥤ C₄` and `G₂₃ : C₂ ⥤ C₃ ⥤ C₄`, this is
the trifunctor `C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄` obtained by composition. -/
@[simps]
def bifunctorComp₂₃ : C₁ ⥤ C₂ ⥤ C₃ ⥤ C₄ 
goal: (((CategoryTheory.bifunctorComp₂₃ F G₂₃).map φ).app X₂).app X₃ = (F.map φ).app ((G₂₃.obj X₂).obj X₃)