File: Mathlib/CategoryTheory/Bicategory/Extension.lean

full_name: CategoryTheory.Bicategory.LeftExtension
code: /-- Triangle diagrams for (left) extensions.
```
  b
  △ \
  |   \ extension  △
f |     \          | unit
  |       ◿
  a - - - ▷ c
      g
```
-/
abbrev LeftExtension (f : a ⟶ b) (g : a ⟶ c) 
goal: Type (max v w)

full_name: CategoryTheory.Bicategory.LeftExtension.extension
code: /-- The extension of `g` along `f`. -/
abbrev extension (t : LeftExtension f g) : b ⟶ c 
goal: b ⟶ c

full_name: CategoryTheory.Bicategory.LeftExtension.unit
code: /-- The 2-morphism filling the triangle diagram. -/
abbrev unit (t : LeftExtension f g) : g ⟶ f ≫ t.extension 
goal: g ⟶ CategoryTheory.CategoryStruct.comp f t.extension

full_name: CategoryTheory.Bicategory.LeftExtension.mk
code: /-- Construct a left extension from a 1-morphism and a 2-morphism. -/
abbrev mk (h : b ⟶ c) (unit : g ⟶ f ≫ h) : LeftExtension f g 
goal: CategoryTheory.Bicategory.LeftExtension f g

full_name: CategoryTheory.Bicategory.LeftExtension.homMk
code: /-- To construct a morphism between left extensions, we need a 2-morphism between the extensions,
and to check that it is compatible with the units. -/
abbrev homMk (η : s.extension ⟶ t.extension) (w : s.unit ≫ f ◁ η = t.unit := by aesop_cat) :
    s ⟶ t 
goal: s ⟶ t

full_name: CategoryTheory.Bicategory.LeftExtension.w
code: @[reassoc (attr := simp)]
theorem w (η : s ⟶ t) : s.unit ≫ f ◁ η.right = t.unit 
goal: CategoryTheory.CategoryStruct.comp s.unit (CategoryTheory.Bicategory.whiskerLeft f η.right) = t.unit

full_name: CategoryTheory.Bicategory.LeftExtension.alongId
code: /-- The left extension along the identity. -/
def alongId (g : a ⟶ c) : LeftExtension (𝟙 a) g 
goal: CategoryTheory.Bicategory.LeftExtension (CategoryTheory.CategoryStruct.id a) g

full_name: CategoryTheory.Bicategory.LeftExtension.instInhabitedId
code: instance : Inhabited (LeftExtension (𝟙 a) g) 
goal: Inhabited (CategoryTheory.Bicategory.LeftExtension (CategoryTheory.CategoryStruct.id a) g)

full_name: CategoryTheory.Bicategory.LeftExtension.ofCompId_right
code: /-- Construct a left extension of `g : a ⟶ c` from a left extension of `g ≫ 𝟙 c`. -/
@[simps!]
def ofCompId (t : LeftExtension f (g ≫ 𝟙 c)) : LeftExtension f g 
goal: t.ofCompId.right = t.extension

full_name: CategoryTheory.Bicategory.LeftExtension.ofCompId_hom
code: /-- Construct a left extension of `g : a ⟶ c` from a left extension of `g ≫ 𝟙 c`. -/
@[simps!]
def ofCompId (t : LeftExtension f (g ≫ 𝟙 c)) : LeftExtension f g 
goal: t.ofCompId.hom = CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.rightUnitor g).inv t.unit

full_name: CategoryTheory.Bicategory.LeftExtension.ofCompId
code: /-- Construct a left extension of `g : a ⟶ c` from a left extension of `g ≫ 𝟙 c`. -/
@[simps!]
def ofCompId (t : LeftExtension f (g ≫ 𝟙 c)) : LeftExtension f g 
goal: CategoryTheory.Bicategory.LeftExtension f g

full_name: CategoryTheory.Bicategory.LeftExtension.ofCompId_left_as
code: /-- Construct a left extension of `g : a ⟶ c` from a left extension of `g ≫ 𝟙 c`. -/
@[simps!]
def ofCompId (t : LeftExtension f (g ≫ 𝟙 c)) : LeftExtension f g 
goal: t.ofCompId.left.as = PUnit.unit

full_name: CategoryTheory.Bicategory.LeftExtension.whisker
code: /-- Whisker a 1-morphism to an extension.
```
  b
  △ \
  |   \ extension  △
f |     \          | unit
  |       ◿
  a - - - ▷ c - - - ▷ x
      g         h
```
-/
def whisker (t : LeftExtension f g) {x : B} (h : c ⟶ x) : LeftExtension f (g ≫ h) 
goal: CategoryTheory.Bicategory.LeftExtension f (CategoryTheory.CategoryStruct.comp g h)

full_name: CategoryTheory.Bicategory.LeftExtension.whisker_extension
code: @[simp]
theorem whisker_extension (t : LeftExtension f g) {x : B} (h : c ⟶ x) :
    (t.whisker h).extension = t.extension ≫ h 
goal: (t.whisker h).extension = CategoryTheory.CategoryStruct.comp t.extension h

full_name: CategoryTheory.Bicategory.LeftExtension.whisker_unit
code: @[simp]
theorem whisker_unit (t : LeftExtension f g) {x : B} (h : c ⟶ x) :
    (t.whisker h).unit = t.unit ▷ h ≫ (α_ f t.extension h).hom 
goal: (t.whisker h).unit =
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight t.unit h)
    (CategoryTheory.Bicategory.associator f t.extension h).hom

full_name: CategoryTheory.Bicategory.LeftExtension.whiskering_obj
code: /-- Whiskering a 1-morphism is a functor. -/
@[simps]
def whiskering {x : B} (h : c ⟶ x) : LeftExtension f g ⥤ LeftExtension f (g ≫ h) 
goal: (CategoryTheory.Bicategory.LeftExtension.whiskering h).obj t = t.whisker h

full_name: CategoryTheory.Bicategory.LeftExtension.whiskering
code: /-- Whiskering a 1-morphism is a functor. -/
@[simps]
def whiskering {x : B} (h : c ⟶ x) : LeftExtension f g ⥤ LeftExtension f (g ≫ h) 
goal: CategoryTheory.Functor (CategoryTheory.Bicategory.LeftExtension f g)
  (CategoryTheory.Bicategory.LeftExtension f (CategoryTheory.CategoryStruct.comp g h))

full_name: CategoryTheory.Bicategory.LeftExtension.whiskering_map
code: /-- Whiskering a 1-morphism is a functor. -/
@[simps]
def whiskering {x : B} (h : c ⟶ x) : LeftExtension f g ⥤ LeftExtension f (g ≫ h) 
goal: ∀ {X Y : CategoryTheory.Bicategory.LeftExtension f g} (η : X ⟶ Y),
  (CategoryTheory.Bicategory.LeftExtension.whiskering h).map η =
    CategoryTheory.Bicategory.LeftExtension.homMk (CategoryTheory.Bicategory.whiskerRight η.right h) ⋯

full_name: CategoryTheory.Bicategory.LeftExtension.whiskerIdCancel_right
code: /-- Define a morphism between left extensions by cancelling the whiskered identities. -/
@[simps! right]
def whiskerIdCancel
    (s : LeftExtension f (g ≫ 𝟙 c)) {t : LeftExtension f g} (τ : s ⟶ t.whisker (𝟙 c)) :
    s.ofCompId ⟶ t 
goal: (s.whiskerIdCancel τ).right =
  CategoryTheory.CategoryStruct.comp τ.right (CategoryTheory.Bicategory.rightUnitor t.extension).hom

full_name: CategoryTheory.Bicategory.LeftExtension.whiskerIdCancel
code: /-- Define a morphism between left extensions by cancelling the whiskered identities. -/
@[simps! right]
def whiskerIdCancel
    (s : LeftExtension f (g ≫ 𝟙 c)) {t : LeftExtension f g} (τ : s ⟶ t.whisker (𝟙 c)) :
    s.ofCompId ⟶ t 
goal: s.ofCompId ⟶ t

full_name: CategoryTheory.Bicategory.LeftExtension.whiskerHom
code: /-- Construct a morphism between whiskered extensions. -/
@[simps! right]
def whiskerHom (i : s ⟶ t) {x : B} (h : c ⟶ x) :
    s.whisker h ⟶ t.whisker h 
goal: s.whisker h ⟶ t.whisker h

full_name: CategoryTheory.Bicategory.LeftExtension.whiskerHom_right
code: /-- Construct a morphism between whiskered extensions. -/
@[simps! right]
def whiskerHom (i : s ⟶ t) {x : B} (h : c ⟶ x) :
    s.whisker h ⟶ t.whisker h 
goal: (CategoryTheory.Bicategory.LeftExtension.whiskerHom i h).right = CategoryTheory.Bicategory.whiskerRight i.right h

full_name: CategoryTheory.Bicategory.LeftExtension.whiskerIso
code: /-- Construct an isomorphism between whiskered extensions. -/
def whiskerIso (i : s ≅ t) {x : B} (h : c ⟶ x) :
    s.whisker h ≅ t.whisker h 
goal: s.whisker h ≅ t.whisker h

full_name: CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_inv_right
code: /-- The isomorphism between left extensions induced by a right unitor. -/
@[simps! hom_right inv_right]
def whiskerOfCompIdIsoSelf (t : LeftExtension f g) : (t.whisker (𝟙 c)).ofCompId ≅ t 
goal: t.whiskerOfCompIdIsoSelf.inv.right = (CategoryTheory.Bicategory.rightUnitor t.extension).inv

full_name: CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf_hom_right
code: /-- The isomorphism between left extensions induced by a right unitor. -/
@[simps! hom_right inv_right]
def whiskerOfCompIdIsoSelf (t : LeftExtension f g) : (t.whisker (𝟙 c)).ofCompId ≅ t 
goal: t.whiskerOfCompIdIsoSelf.hom.right = (CategoryTheory.Bicategory.rightUnitor t.extension).hom

full_name: CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf
code: /-- The isomorphism between left extensions induced by a right unitor. -/
@[simps! hom_right inv_right]
def whiskerOfCompIdIsoSelf (t : LeftExtension f g) : (t.whisker (𝟙 c)).ofCompId ≅ t 
goal: (t.whisker (CategoryTheory.CategoryStruct.id c)).ofCompId ≅ t

full_name: CategoryTheory.Bicategory.LeftLift
code: /-- Triangle diagrams for (left) lifts.
```
            b
          ◹ |
   lift /   |      △
      /     | f    | unit
    /       ▽
  c - - - ▷ a
       g
```
-/
abbrev LeftLift (f : b ⟶ a) (g : c ⟶ a) 
goal: Type (max v w)

full_name: CategoryTheory.Bicategory.LeftLift.lift
code: /-- The lift of `g` along `f`. -/
abbrev lift (t : LeftLift f g) : c ⟶ b 
goal: c ⟶ b

full_name: CategoryTheory.Bicategory.LeftLift.unit
code: /-- The 2-morphism filling the triangle diagram. -/
abbrev unit (t : LeftLift f g) : g ⟶ t.lift ≫ f 
goal: g ⟶ CategoryTheory.CategoryStruct.comp t.lift f

full_name: CategoryTheory.Bicategory.LeftLift.mk
code: /-- Construct a left lift from a 1-morphism and a 2-morphism. -/
abbrev mk (h : c ⟶ b) (unit : g ⟶ h ≫ f) : LeftLift f g 
goal: CategoryTheory.Bicategory.LeftLift f g

full_name: CategoryTheory.Bicategory.LeftLift.homMk
code: /-- To construct a morphism between left lifts, we need a 2-morphism between the lifts,
and to check that it is compatible with the units. -/
abbrev homMk (η : s.lift ⟶ t.lift) (w : s.unit ≫ η ▷ f = t.unit := by aesop_cat) :
    s ⟶ t 
goal: s ⟶ t

full_name: CategoryTheory.Bicategory.LeftLift.w
code: @[reassoc (attr := simp)]
theorem w (h : s ⟶ t) : s.unit ≫ h.right ▷ f = t.unit 
goal: CategoryTheory.CategoryStruct.comp s.unit (CategoryTheory.Bicategory.whiskerRight h.right f) = t.unit

full_name: CategoryTheory.Bicategory.LeftLift.alongId
code: /-- The left lift along the identity. -/
def alongId (g : c ⟶ a) : LeftLift (𝟙 a) g 
goal: CategoryTheory.Bicategory.LeftLift (CategoryTheory.CategoryStruct.id a) g

full_name: CategoryTheory.Bicategory.LeftLift.instInhabitedId
code: instance : Inhabited (LeftLift (𝟙 a) g) 
goal: Inhabited (CategoryTheory.Bicategory.LeftLift (CategoryTheory.CategoryStruct.id a) g)

full_name: CategoryTheory.Bicategory.LeftLift.ofIdComp
code: /-- Construct a left lift along `g : c ⟶ a` from a left lift along `𝟙 c ≫ g`. -/
@[simps!]
def ofIdComp (t : LeftLift f (𝟙 c ≫ g)) : LeftLift f g 
goal: CategoryTheory.Bicategory.LeftLift f g

full_name: CategoryTheory.Bicategory.LeftLift.ofIdComp_right
code: /-- Construct a left lift along `g : c ⟶ a` from a left lift along `𝟙 c ≫ g`. -/
@[simps!]
def ofIdComp (t : LeftLift f (𝟙 c ≫ g)) : LeftLift f g 
goal: t.ofIdComp.right = t.lift

full_name: CategoryTheory.Bicategory.LeftLift.ofIdComp_hom
code: /-- Construct a left lift along `g : c ⟶ a` from a left lift along `𝟙 c ≫ g`. -/
@[simps!]
def ofIdComp (t : LeftLift f (𝟙 c ≫ g)) : LeftLift f g 
goal: t.ofIdComp.hom = CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.leftUnitor g).inv t.unit

full_name: CategoryTheory.Bicategory.LeftLift.ofIdComp_left_as
code: /-- Construct a left lift along `g : c ⟶ a` from a left lift along `𝟙 c ≫ g`. -/
@[simps!]
def ofIdComp (t : LeftLift f (𝟙 c ≫ g)) : LeftLift f g 
goal: t.ofIdComp.left.as = PUnit.unit

full_name: CategoryTheory.Bicategory.LeftLift.whisker
code: /-- Whisker a 1-morphism to a lift.
```
                    b
                  ◹ |
           lift /   |      △
              /     | f    | unit
            /       ▽
x - - - ▷ c - - - ▷ a
     h         g
```
-/
def whisker (t : LeftLift f g) {x : B} (h : x ⟶ c) : LeftLift f (h ≫ g) 
goal: CategoryTheory.Bicategory.LeftLift f (CategoryTheory.CategoryStruct.comp h g)

full_name: CategoryTheory.Bicategory.LeftLift.whisker_lift
code: @[simp]
theorem whisker_lift (t : LeftLift f g) {x : B} (h : x ⟶ c) :
    (t.whisker h).lift = h ≫ t.lift 
goal: (t.whisker h).lift = CategoryTheory.CategoryStruct.comp h t.lift

full_name: CategoryTheory.Bicategory.LeftLift.whisker_unit
code: @[simp]
theorem whisker_unit (t : LeftLift f g) {x : B} (h : x ⟶ c) :
    (t.whisker h).unit = h ◁ t.unit ≫ (α_ h t.lift f).inv 
goal: (t.whisker h).unit =
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft h t.unit)
    (CategoryTheory.Bicategory.associator h t.lift f).inv

full_name: CategoryTheory.Bicategory.LeftLift.whiskering_map
code: /-- Whiskering a 1-morphism is a functor. -/
@[simps]
def whiskering {x : B} (h : x ⟶ c) : LeftLift f g ⥤ LeftLift f (h ≫ g) 
goal: ∀ {X Y : CategoryTheory.Bicategory.LeftLift f g} (η : X ⟶ Y),
  (CategoryTheory.Bicategory.LeftLift.whiskering h).map η =
    CategoryTheory.Bicategory.LeftLift.homMk (CategoryTheory.Bicategory.whiskerLeft h η.right) ⋯

full_name: CategoryTheory.Bicategory.LeftLift.whiskering_obj
code: /-- Whiskering a 1-morphism is a functor. -/
@[simps]
def whiskering {x : B} (h : x ⟶ c) : LeftLift f g ⥤ LeftLift f (h ≫ g) 
goal: (CategoryTheory.Bicategory.LeftLift.whiskering h).obj t = t.whisker h

full_name: CategoryTheory.Bicategory.LeftLift.whiskering
code: /-- Whiskering a 1-morphism is a functor. -/
@[simps]
def whiskering {x : B} (h : x ⟶ c) : LeftLift f g ⥤ LeftLift f (h ≫ g) 
goal: CategoryTheory.Functor (CategoryTheory.Bicategory.LeftLift f g)
  (CategoryTheory.Bicategory.LeftLift f (CategoryTheory.CategoryStruct.comp h g))

full_name: CategoryTheory.Bicategory.LeftLift.whiskerIdCancel_right
code: /-- Define a morphism between left lifts by cancelling the whiskered identities. -/
@[simps! right]
def whiskerIdCancel
    (s : LeftLift f (𝟙 c ≫ g)) {t : LeftLift f g} (τ : s ⟶ t.whisker (𝟙 c)) :
    s.ofIdComp ⟶ t 
goal: (s.whiskerIdCancel τ).right =
  CategoryTheory.CategoryStruct.comp τ.right (CategoryTheory.Bicategory.leftUnitor t.lift).hom

full_name: CategoryTheory.Bicategory.LeftLift.whiskerIdCancel
code: /-- Define a morphism between left lifts by cancelling the whiskered identities. -/
@[simps! right]
def whiskerIdCancel
    (s : LeftLift f (𝟙 c ≫ g)) {t : LeftLift f g} (τ : s ⟶ t.whisker (𝟙 c)) :
    s.ofIdComp ⟶ t 
goal: s.ofIdComp ⟶ t

full_name: CategoryTheory.Bicategory.LeftLift.whiskerHom
code: /-- Construct a morphism between whiskered lifts. -/
@[simps! right]
def whiskerHom (i : s ⟶ t) {x : B} (h : x ⟶ c) :
    s.whisker h ⟶ t.whisker h 
goal: s.whisker h ⟶ t.whisker h

full_name: CategoryTheory.Bicategory.LeftLift.whiskerHom_right
code: /-- Construct a morphism between whiskered lifts. -/
@[simps! right]
def whiskerHom (i : s ⟶ t) {x : B} (h : x ⟶ c) :
    s.whisker h ⟶ t.whisker h 
goal: (CategoryTheory.Bicategory.LeftLift.whiskerHom i h).right = CategoryTheory.Bicategory.whiskerLeft h i.right

full_name: CategoryTheory.Bicategory.LeftLift.whiskerIso
code: /-- Construct an isomorphism between whiskered lifts. -/
def whiskerIso (i : s ≅ t) {x : B} (h : x ⟶ c) :
    s.whisker h ≅ t.whisker h 
goal: s.whisker h ≅ t.whisker h

full_name: CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_hom_right
code: /-- The isomorphism between left lifts induced by a left unitor. -/
@[simps! hom_right inv_right]
def whiskerOfIdCompIsoSelf (t : LeftLift f g) : (t.whisker (𝟙 c)).ofIdComp ≅ t 
goal: t.whiskerOfIdCompIsoSelf.hom.right = (CategoryTheory.Bicategory.leftUnitor t.lift).hom

full_name: CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf_inv_right
code: /-- The isomorphism between left lifts induced by a left unitor. -/
@[simps! hom_right inv_right]
def whiskerOfIdCompIsoSelf (t : LeftLift f g) : (t.whisker (𝟙 c)).ofIdComp ≅ t 
goal: t.whiskerOfIdCompIsoSelf.inv.right = (CategoryTheory.Bicategory.leftUnitor t.lift).inv

full_name: CategoryTheory.Bicategory.LeftLift.whiskerOfIdCompIsoSelf
code: /-- The isomorphism between left lifts induced by a left unitor. -/
@[simps! hom_right inv_right]
def whiskerOfIdCompIsoSelf (t : LeftLift f g) : (t.whisker (𝟙 c)).ofIdComp ≅ t 
goal: (t.whisker (CategoryTheory.CategoryStruct.id c)).ofIdComp ≅ t

full_name: CategoryTheory.Bicategory.RightExtension
code: /-- Triangle diagrams for (right) extensions.
```
  b
  △ \
  |   \ extension  | counit
f |     \          ▽
  |       ◿
  a - - - ▷ c
      g
```
-/
abbrev RightExtension (f : a ⟶ b) (g : a ⟶ c) 
goal: Type (max v w)

full_name: CategoryTheory.Bicategory.RightExtension.extension
code: /-- The extension of `g` along `f`. -/
abbrev extension (t : RightExtension f g) : b ⟶ c 
goal: b ⟶ c

full_name: CategoryTheory.Bicategory.RightExtension.counit
code: /-- The 2-morphism filling the triangle diagram. -/
abbrev counit (t : RightExtension f g) : f ≫ t.extension ⟶ g 
goal: CategoryTheory.CategoryStruct.comp f t.extension ⟶ g

full_name: CategoryTheory.Bicategory.RightExtension.mk
code: /-- Construct a right extension from a 1-morphism and a 2-morphism. -/
abbrev mk (h : b ⟶ c) (counit : f ≫ h ⟶ g) : RightExtension f g 
goal: CategoryTheory.Bicategory.RightExtension f g

full_name: CategoryTheory.Bicategory.RightExtension.homMk
code: /-- To construct a morphism between right extensions, we need a 2-morphism between the extensions,
and to check that it is compatible with the counits. -/
abbrev homMk {s t : RightExtension f g} (η : s.extension ⟶ t.extension)
    (w : f ◁ η ≫ t.counit = s.counit) : s ⟶ t 
goal: s ⟶ t

full_name: CategoryTheory.Bicategory.RightExtension.w
code: @[reassoc (attr := simp)]
theorem w {s t : RightExtension f g} (η : s ⟶ t) :
    f ◁ η.left ≫ t.counit = s.counit 
goal: CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft f η.left) t.counit = s.counit

full_name: CategoryTheory.Bicategory.RightExtension.alongId
code: /-- The right extension along the identity. -/
def alongId (g : a ⟶ c) : RightExtension (𝟙 a) g 
goal: CategoryTheory.Bicategory.RightExtension (CategoryTheory.CategoryStruct.id a) g

full_name: CategoryTheory.Bicategory.RightExtension.instInhabitedId
code: instance : Inhabited (RightExtension (𝟙 a) g) 
goal: Inhabited (CategoryTheory.Bicategory.RightExtension (CategoryTheory.CategoryStruct.id a) g)

full_name: CategoryTheory.Bicategory.RightLift
code: /-- Triangle diagrams for (right) lifts.
```
            b
          ◹ |
   lift /   |      | counit
      /     | f    ▽
    /       ▽
  c - - - ▷ a
       g
```
-/
abbrev RightLift (f : b ⟶ a) (g : c ⟶ a) 
goal: Type (max v w)

full_name: CategoryTheory.Bicategory.RightLift.lift
code: /-- The lift of `g` along `f`. -/
abbrev lift (t : RightLift f g) : c ⟶ b 
goal: c ⟶ b

full_name: CategoryTheory.Bicategory.RightLift.counit
code: /-- The 2-morphism filling the triangle diagram. -/
abbrev counit (t : RightLift f g) : t.lift ≫ f ⟶ g 
goal: CategoryTheory.CategoryStruct.comp t.lift f ⟶ g

full_name: CategoryTheory.Bicategory.RightLift.mk
code: /-- Construct a right lift from a 1-morphism and a 2-morphism. -/
abbrev mk (h : c ⟶ b) (counit : h ≫ f ⟶ g) : RightLift f g 
goal: CategoryTheory.Bicategory.RightLift f g

full_name: CategoryTheory.Bicategory.RightLift.homMk
code: /-- To construct a morphism between right lifts, we need a 2-morphism between the lifts,
and to check that it is compatible with the counits. -/
abbrev homMk {s t : RightLift f g} (η : s.lift ⟶ t.lift) (w : η ▷ f ≫ t.counit = s.counit) :
    s ⟶ t 
goal: s ⟶ t

full_name: CategoryTheory.Bicategory.RightLift.w
code: @[reassoc (attr := simp)]
theorem w {s t : RightLift f g} (h : s ⟶ t) :
    h.left ▷ f ≫ t.counit = s.counit 
goal: CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight h.left f) t.counit = s.counit

full_name: CategoryTheory.Bicategory.RightLift.alongId
code: /-- The right lift along the identity. -/
def alongId (g : c ⟶ a) : RightLift (𝟙 a) g 
goal: CategoryTheory.Bicategory.RightLift (CategoryTheory.CategoryStruct.id a) g

full_name: CategoryTheory.Bicategory.RightLift.instInhabitedId
code: instance : Inhabited (RightLift (𝟙 a) g) 
goal: Inhabited (CategoryTheory.Bicategory.RightLift (CategoryTheory.CategoryStruct.id a) g)