Theorems · Definition · linear algebra

Submodule.quotientPiLift

{ι : Type u_1} →
  {R : Type u_2} →
    [inst : CommRing R] →
      {Ms : ι → Type u_3} →
        [inst_1 : (i : ι) → AddCommGroup (Ms i)] →
          [inst_2 : (i : ι) → Module R (Ms i)] →
            {Ns : ι → Type u_5} →
              [inst_3 : (i : ι) → AddCommGroup (Ns i)] →
                [inst_4 : (i : ι) → Module R (Ns i)] →
                  (p : (i : ι) → Submodule R (Ms i)) →
                    (f : (i : ι) → Ms i →ₗ[R] Ns i) →
                      (∀ (i : ι), p i ≤ (f i).ker) → ((i : ι) → Ms i) ⧸ Submodule.pi Set.univ p →ₗ[R] (i : ι) → Ns i

Lift a family of maps to a quotient of direct sums.

Defined in

Mathlib.LinearAlgebra.Quotient.Pi

Cited by

6 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule