Theorems · Definition · commutative algebra

IsAdicComplete.StrictMono.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 • ⊤) →
                        (∀ {m : ℕ}, Submodule.factorPow I N ⋯ ∘ₗ f (m + 1) = f m) → [IsAdicComplete I N] → M →ₗ[R] N

A variant of IsAdicComplete.lift. Only takes f n : M →ₗ[R] N ⧸ (I ^ (a n) • ⊤) from a strictly increasing sequence a n.

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleIsAdicComplete