| import Mathlib | |
| open CategoryTheory Limits Opposite | |
| variable (p : ℕ) | |
| noncomputable def pAdicFunctor : ℕᵒᵖ ⥤ RingCat where | |
| obj n := RingCat.of (ZMod (p ^ (unop n))) | |
| map {m n} f := RingCat.ofHom <| | |
| ZMod.castHom (pow_dvd_pow p (leOfHom f.unop)) (ZMod (p ^ (unop n))) | |
| map_id := by | |
| intro n | |
| ext x | |
| simp | |
| map_comp := by | |
| intro x y z f g | |
| ext x | |
| simp | |
| theorem pAdic_limit_exists : HasLimit (pAdicFunctor p) := by | |
| sorry |