Theorems · Definition · commutative algebra

IsAdicComplete.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] →
                  [IsAdicComplete I N] →
                    (f : (n : ℕ) → M →ₗ[R] N ⧸ I ^ n • ⊤) →
                      (∀ {m n : ℕ} (hle : m ≤ n), Submodule.factorPow I N hle ∘ₗ f n = f m) → M →ₗ[R] N

Universal property of IsAdicComplete. The lift linear map lift I f h : M →ₗ[R] N of a sequence of compatible linear maps f n : M →ₗ[R] N ⧸ (I ^ n • ⊤).

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

6 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleIsAdicComplete