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916823d | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | 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 |