Theorems · Definition · commutative algebra

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

Lift a compatible family of linear maps M →ₗ[R] N ⧸ (I ^ n • ⊤ : Submodule R N) to the I-adic completion of M.

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

9 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule