Theorems · Theorem · commutative algebra

IsAdicComplete.StrictMono.eq_lift

∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {N : Type u_5} [inst_3 : AddCommGroup N] [inst_4 : Module R N] {a : ℕ → ℕ} (ha : StrictMono a)
  (f : (n : ℕ) → M →ₗ[R] N ⧸ I ^ a n • ⊤) (hf : ∀ {m : ℕ}, Submodule.factorPow I N ⋯ ∘ₗ f (m + 1) = f m)
  [inst_5 : IsAdicComplete I N] {F : M →ₗ[R] N},
  (∀ (n : ℕ), (I ^ a n • ⊤).mkQ ∘ₗ F = f n) → F = IsAdicComplete.StrictMono.lift I ha f ⋯

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

0 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleIsAdicComplete