| import Mathlib | |
| open CategoryTheory | |
| def functor_involution : Grp.{u} ⥤ Type u where | |
| obj := fun G => { g : G.carrier | g * g = 1 } | |
| map := fun {G H} f x => ⟨f.hom x.val, by | |
| refine Set.mem_setOf.mpr ?_ | |
| rcases x with ⟨g, hg⟩ | |
| simp only [Set.mem_setOf_eq] at hg | |
| rw [← f.hom.map_mul, hg] | |
| simp only [map_one] | |
| ⟩ | |
| theorem involution_functor_representable : | |
| CategoryTheory.Functor.IsCorepresentable functor_involution := by | |
| sorry |