C : Type u₁
inst✝¹ : Category C
D : Type u₂
inst✝ : Category D
e : C ≌ D
X : C
⊢ 𝟙 (e.functor.obj X) = 𝟙 (e.functor.obj ((𝟭 C).obj X))
C : Type u₁
inst✝¹ : Category C
D : Type u₂
inst✝ : Category D
e : C ≌ D
X : C
⊢ (counit e).app (e.functor.obj X) = e.functor.map ((unitInv e).app X)
erw [← Iso.hom_comp_eq_id (e.functor.mapIso (e.unitIso.app X)), functor_unit_comp]
no goals
C : Type u₁
inst✝¹ : Category C
D : Type u₂
inst✝ : Category D
e : C ≌ D
X : C
⊢ 𝟙 (e.functor.obj X) = 𝟙 (e.functor.obj ((𝟭 C).obj X))
rfl