V : Type u
inst✝² : Quiver V
V' : Type u'
inst✝¹ : Quiver V'
V'' : Type u''
inst✝ : Quiver V''
φ : V ⥤q V'
φ' : V' ⥤q V''
⊢ lift (φ ⋙q φ' ⋙q of V'') = lift (φ ⋙q of V') ⋙ lift (φ' ⋙q of V'')
V : Type u
inst✝² : Quiver V
V' : Type u'
inst✝¹ : Quiver V'
V'' : Type u''
inst✝ : Quiver V''
φ : V ⥤q V'
φ' : V' ⥤q V''
⊢ freeGroupoidFunctor (φ ⋙q φ') = freeGroupoidFunctor φ ⋙ freeGroupoidFunctor φ'
dsimp only [freeGroupoidFunctor]
V : Type u
inst✝² : Quiver V
V' : Type u'
inst✝¹ : Quiver V'
V'' : Type u''
inst✝ : Quiver V''
φ : V ⥤q V'
φ' : V' ⥤q V''
⊢ lift (φ ⋙q of V') ⋙ lift (φ' ⋙q of V'') = lift (φ ⋙q φ' ⋙q of V'')
V : Type u
inst✝² : Quiver V
V' : Type u'
inst✝¹ : Quiver V'
V'' : Type u''
inst✝ : Quiver V''
φ : V ⥤q V'
φ' : V' ⥤q V''
⊢ lift (φ ⋙q φ' ⋙q of V'') = lift (φ ⋙q of V') ⋙ lift (φ' ⋙q of V'')
symm
case hΦ
V : Type u
inst✝² : Quiver V
V' : Type u'
inst✝¹ : Quiver V'
V'' : Type u''
inst✝ : Quiver V''
φ : V ⥤q V'
φ' : V' ⥤q V''
⊢ of V ⋙q (lift (φ ⋙q of V') ⋙ lift (φ' ⋙q of V'')).toPrefunctor = φ ⋙q φ' ⋙q of V''
V : Type u
inst✝² : Quiver V
V' : Type u'
inst✝¹ : Quiver V'
V'' : Type u''
inst✝ : Quiver V''
φ : V ⥤q V'
φ' : V' ⥤q V''
⊢ lift (φ ⋙q of V') ⋙ lift (φ' ⋙q of V'') = lift (φ ⋙q φ' ⋙q of V'')
apply lift_unique
no goals
case hΦ
V : Type u
inst✝² : Quiver V
V' : Type u'
inst✝¹ : Quiver V'
V'' : Type u''
inst✝ : Quiver V''
φ : V ⥤q V'
φ' : V' ⥤q V''
⊢ of V ⋙q (lift (φ ⋙q of V') ⋙ lift (φ' ⋙q of V'')).toPrefunctor = φ ⋙q φ' ⋙q of V''
rfl