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916823d | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | 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 |