Theorems · Theorem · linear algebra

Submodule.pi_liftQ_eq_liftQ_pi

∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {ι : Type u_5}
  {N : ι → Type u_6} [inst_3 : (i : ι) → AddCommGroup (N i)] [inst_4 : (i : ι) → Module R (N i)]
  (f : (i : ι) → M →ₗ[R] N i) {p : Submodule R M} (h : ∀ (i : ι), p ≤ (f i).ker),
  (LinearMap.pi fun i => p.liftQ (f i) ⋯) = p.liftQ (LinearMap.pi f) ⋯

Defined in

Mathlib.LinearAlgebra.Quotient.Basic

Cited by

1 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddCommGroupModule