Theorems · Theorem · commutative algebra

IsAdicComplete.of_liftRingHom

∀ {R : Type u_1} {S : Type u_2} [inst : NonAssocSemiring R] [inst_1 : CommRing S] (I : Ideal S)
  [inst_2 : IsAdicComplete I S] (f : (n : ℕ) → R →+* S ⧸ I ^ n)
  (hf : ∀ {m n : ℕ} (hle : m ≤ n), (Ideal.Quotient.factorPow I hle).comp (f n) = f m) (x : R),
  (AdicCompletion.of I S) ((IsAdicComplete.liftRingHom I f ⋯) x) = (AdicCompletion.liftRingHom I f ⋯) x

Defined in

Mathlib.RingTheory.AdicCompletion.RingHom

Cited by

1 results in Mathlib

Foundations

Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonAssocSemiringCommRingIsAdicComplete