Theorems · Theorem · commutative algebra

IsAdicComplete.mk_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] [inst_5 : IsAdicComplete I N]
  {f : (n : ℕ) → M →ₗ[R] N ⧸ I ^ n • ⊤} (h : ∀ {m n : ℕ} (hle : m ≤ n), Submodule.factorPow I N hle ∘ₗ f n = f m)
  (n : ℕ) (x : M), Submodule.Quotient.mk ((IsAdicComplete.lift I f ⋯) x) = (f n) x

The composition of lift linear map lift I f h : M →ₗ[R] N with the canonical projection N → N ⧸ (I ^ n • ⊤) is f n .

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

2 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleIsAdicComplete